If they fail this save what will happen?
They will fall into the trap. Simple as that. This also means they get a save against the illusion, and if they fail this save, the illusion is still "real" and they may fall into another trap in that room.
The behavior of illusions are subjective
The magic school of illusions is complex not only because the relative power of each spell has to be adjucated by the GM, but because their usefulness is limited only by the caster's creativity.
It's important to note that Mirage Arcana, which works like Hallucinatory Terrain, will conceal and/or alter structures in the room:
You make natural terrain look, sound, and smell like some other sort of natural terrain. Structures, equipment, and creatures within the area are not hidden or changed in appearance.
Unlike hallucinatory terrain, the spell can alter the appearance of structures (or add them where none are present).
In other words, you can create and/or hide any of the following: rooms, windows, tables, chairs, tripwires, trapdoors, swinging blades and any variety of traps that will be completely concealed visually, by sound, by smell, and by tactile feedback.
So a Pit Trap won't even allow a perception check to notice the false floor, should the character be looking for traps and fail his Will check, because he won't notice the sensory hints (wires, undusted area, hingers, different colors, different texture, etc) indicating that there is a trap there.
And all of this is due to the illusion being a Glamer, which means that the spell isn't exactly affecting your mind, but affecting your senses, which may be harder to ignore. You can't exactly ignore a smell or the texture you are touching simply by telling yourself to ignore it. Even if you are told "this smell is an illusion", you are still sensing it, and will get another Will check with +4 because of the help.
A glamer spell changes a subject’s sensory qualities, making it look, feel, taste, smell, or sound like something else, or even seem to disappear.
Also, quoting Ultimate Intrigue's guidelines about illusions (p. 158):
Phantasms directly assail a creature’s mind, so the creature automatically and immediately receives a saving throw to disbelieve a phantasm. Figments and glamers, however, have the more difficult-to-adjudicate rule that creatures receive a saving throw to disbelieve only if they “interact” with the illusion.
There are no clear guidelines of what is enough proof
It is commonly accepted that spending some time analyzing the illusion's behavior against all sort of interactions should allow you to either make another saving throw, or to disbelieve it automatically. But each illusion has different parameters, some actually have tactile feedback (which is the case for Mirage Arcana), as such, if you simply poke the ground with a stick, it will not reveal the spell to be an illusion, but should be enough to allow a saving throw, as you are interacting with the illusion.
A character can't exactly tell if the wall they are touching, which allows their hand to go through, is really an illusion or simply some kind of incorporeal wall. And it's even worse if you see another character walk through a wall, as they might be using some spell that allows them to walk through walls, or become incorporeal, or teleport using stones. Are you really willing to risk walking over an "illusionary" pit simply because someone else walked over it? What proof there is that this guy simply isn't flying?
It's that kind of proof that the rules are talking about. And since no concrete guidelines are given, that is entirely subject to GM discretion.
On spellcraft to identity spells
According to this FAQ entry, every spell has some kind of visual manifestation that will allow another person to possibly identify what is being cast, which may positively identify the illusion. This doesn't necessary mean that you will automatically disbelieve it, because that would mean that you would get a far stronger benefit from investing in the skill Spellcraft than caring about your Will saving throw, and that you know exactly what the caster was thinking when he was casting the spell, not only identifying the spell, but also identifying the produced effect, which isn't covered by the skill.
If I see the enemy caster cast a spell and I identify it as Mirage Arcana, I will see the terrain changing around me and I will look around... But nothing will look different, because I have not yet interacted with the spell's effect. If suddenly another party member falls into the ground, I will probably think "Oh... a pit spell with a fake 'ground' on top. Clever bastard...", and tell my group "Look out for the concealed pit, guys. It's right over there, but it's covered by an illusion.", which will allow to make their save with +4 bonus.
How I GM illusions
Again, illusions are subjective. This means that each GM will have a different opinion and how they will behave in a specific situation, and your GM's opinion on this may be completely different to mine. Personally, I try to advocate in favor of the illusionist, meaning that the illusion (if using the appropriate subschools) will be real until something in the text allows it to be proven otherwise, which normally requires interaction with the illusion by the rules (see At what point do you count as interacting with an illusion?).
This means that the figment or phantasm of an ogre will not really harm you, and you can disbelieve it as soon as you are either hit or successfully hit the ogre, showing a translucent outline like a hologram still trying to battle. While the glamer or pattern of an ogre will even harm you if you do not make the Will check, possibly causing you to fall unconcious from the illusionary damage that your mind believes that he caused you.
In terms of roleplaying, I try to never tell the players that it was an illusion, even if they pass their check. If they are spellcasters and ask about it, and for some reason haven't figured it out yet, then I ask for a Spellcraft check to realize that there is a spell that does exactly what they just saw (some illusionary effect). Otherwise, they will feel like they are fighting something real, and if disbelieved, something disapears (or becomes translucent), or they feel like they were teleported elsewhere, or that the creature blinked/vanished/teleported away in front of them.
If I don't mention "illusion" they probably won't think "illusion" either. But if they figure it out, kudos to them. But this also means that you will very likely have to make their Will checks, or they will be suspicious of it before it even starts. Since many players are not well fond of the GM making their checks for them, you can describe this as some kind of "fake" effect, which normally works pretty well.
As an example. Once I described a room where a boss battle was about to take place as if the boss's emanated enough energy that the floor and walls were cracking because of it. They took that as literal, and were afraid of the boss before the boss even acted in combat, which allowed me to ask for Will saves to disbelieve the illusions the boss was casting at them and they believed those saves were to avoid some kind of fear aura going on or that energy that I described before the battle begun.
In truth... That was all flavor, there was no real energy doing anything. The boss had a 3rd-party template (from Advanced Bestiary) that infused him with negative energy so much that it was visible around him. And every time he cast Channel Energy (he was technically a negative-energy infused huecuva), I described that energy pulsating in a wave emanating from him, which freaked out my players, and caused more morale damage to the players than to their characters.
Otherwise, pretty much every interaction with illusions (other than Shadows) would either grant that +4 bonus to saves, or be automatically resisted since it's fairly easy to come up with creative solutions as to "why my character doesn't believe it to be real".
Developers on illusions
James Jacobs (Paizo's Creative Director), back during the game's playtest period, told us this in a thread asking for clarifications about disbelieving illusions:
Illusions are, and have always been, kinda tricky and troubling. In my own games, I tend to rule on illusion effects by trying to ensure that someone does something that won't outdo a non-illusion spell of the same level. The more creative a player is, the easier it is for him to use even relatively simple illusions to try to mimic the effects of really powerful things, and that's frustrating to both the GM and to other players, who legitimately earn those real powers.
Put another way: Just because at 5th level you can create a pretty convincing illusion of a pit fiend or a tornado doesn't mean that you should expect your 3rd level spell to duplicate the effects of a gate or control weather spell. At best, you should expect your 3rd level spell to duplicate the effects of any other 3rd level spell's power.
While not directly addressing the issue, it gives us some important direction at how we should rule illusions so they don't become too powerful in the hands of a creative player.
This FAQ about invisibility clarifies that you may or may not see yourself when invisible, subject to GM discretion. Considering that you know that you are invisible, we cannot state (basing ourselves on raw) that "if I know its an illusion I automatically disbelieve it".
Invisibility: Can you see yourself when you're invisible?
The spell doesn't say one way or the other.
Because being invisible doesn't give you penalties on actions that require you to be able to see exactly what you're doing (such as picking a lock), you can assume that you can at least see yourself well enough to perform such actions without penalty. Whether this means you can see yourself as if you were not invisible, can see yourself as a ghostly image, or some other description is up to the GM, so long as the description doesn't hinder your own actions.
If we go further back (2006), and check Skip Willians 3.5e articles about illusions, we get this piece of information:
According to the Player's Handbook, if you're faced with proof that an illusion isn't real, you disbelieve the illusion without making a saving throw. The rules give a few examples of "proof" that an illusion isn't real. If you step on an illusory floor and fall through, you know that floor isn't real. Likewise, if you poke around an illusory floor and your hand (or the implement you're using as a probe) goes through the floor, you know the floor isn't real.
It's worth noting that in both examples the illusion fails to function as a real object would. A real floor is solid. It supports your weight (unless it breaks under you), and you can't push objects or parts of your body through it. A character could create an illusion that reacts appropriately when disturbed (with a programmed image spell, for example). In such cases, a character interacting with the illusion still must make a saving throw to disbelieve the illusion. For example, if you use a programmed image spell to create an illusory floor that collapses when someone touches it or walks in it, that's consistent with the way at least some real floors work and a saving throw is required to disbelieve even when someone falls through it.
The rules don't say so, but if you create an illusion that allows a saving throw for disbelief, you automatically disbelieve it (you know it isn't real because you created it).
Keep in mind that, while useful as insight, those articles are not valid as rules as written or even rules as intended for Pathfinder, but they will help you in areas where the rules are grey and come up with your own interpretation at your table (aka, house rules).
For a complete read, here are the links to all articles: Part 1, Part 2, Part 3 and Part 4;