Armor Class has historically represented your ability to avoid taking the brunt of a hit, not your ability to avoid the hit.
When your characters are in melee, don't assume they're all standing still staring at each other. They're constantly in a state of brawl, swinging blades, trading jabs, parrying, shifting around, etc. This is why there are penalties for Ranged Attacks vs. characters in melee.
What attack actions represent are the notable combat actions that constitute dealing meaningful blow to your opponents. Like two samurai fighting when one breaks away and manages to get a heavy strike in. I'll be using a Samurai Duel as an example throughout this answer.
Let's look at the formula for Armor Class in a past edition. D&D 5e has changed a lot of things, but it still had its beginnings here.
Total AC in D&D 3.5e = 10 + armor bonus + shield bonus + Dexterity modifier + size modifier + deflection bonus + natural armor + dodge bonuses + enhancement bonuses*
Dexterity and Dodge Bonuses
These bonuses contribute how likely you are to dodge an attack outright. In this situation, a Samurai will go in for a strike and the other Samurai will sidestep it.
The size bonus/penalty represents the how your size contributes to a sort-of passive dodge. You're harder to hit when you're small because just your general movements would make you harder to hit. A goblin samurai is shifting back and forth against a human samurai. Since the goblin is small, the human samurai needs to hit a smaller target which is generally harder to do. The goblin isn't trying to dodge, it's just moving around.
Deflection bonuses represent parts of armor or your body that will take a hit and divert most of its force away from you. The shape of the armor-clad samurai's helmet diverts a head strike from an annoyed Ronin.
Armor and Shield Bonuses
Your Armor and Shield Bonuses contribute to how likely an enemy is to hit your armor or shield instead of your actual body.
Natural Armor Bonuses
For when your armor doesn't help, but your rock-hard skin does. Natural armor is the part of your body you don't mind getting hit in. If you've got wood for skin and someone's swinging a katana at you, it could very well get caught in that thick, woody membrane. The Shogun learned this lesson the hard way when when a treefolk swordsman challenged him to duel.
In D&D 5e, a lot of this is unspoken or hidden away
Now, your "Armor Bonus" is masked by being your new "Base Armor". Most modifications to your Armor Class will follow similar logic in terms of what's actually happening when you get attacked. For example, in D&D 5e, Mage Armor changes your Base AC to 13. What this really amounts to is instead of being naked with a Base AC of 10, you've got a +3 chance for an attack to hit your Magic Armor, instead of hitting you. It's still generally the same concept.
Now, back to your goblin example
You said you have 19 AC. Let's say for the sake of a meaningful example, your AC breaks down in the following way:
Magical Leather Armor Rogue: 11 + 4 Dex + 4 from a Magic Item or something.
That base 11 is really 10 from general brawling movement and +1 from actually wearing armor at all. We don't really care what that last +4 is from. Let's say something magic.
Next, let's assume that the Goblin doesn't have any bonus to it's Attack rolls. It rolls a 1d20 and uses that roll only to see if it hits you.
Roll -> What Happens
1 -> They were bad, so they missed.
2 -> You were moving, so they missed.
3 -> You were moving, so they missed.
4 -> You were moving, so they missed.
5 -> You were moving, so they missed.
6 -> You were moving, so they missed.
7 -> You were moving, so they missed.
8 -> You were moving, so they missed.
9 -> You were moving, so they missed.
10 -> They would have hit you, but you passively dodged.
11 -> They would have hit you, but you passively dodged.
12 -> They would have hit you, but you passively dodged.
13 -> They would have hit you, but you passively dodged.
14 -> This cloud of magic catches the blade before it reaches you.
15 -> This cloud of magic catches the blade before it reaches you.
16 -> This cloud of magic catches the blade before it reaches you.
17 -> This cloud of magic catches the blade before it reaches you.
18 -> Blades hit you, but you were wearing enough armor so it didn't reach your body.
19 -> The Goblin cuts you, because it matched your Armor Class.
20 -> The Goblin cuts you, because it beat your Armor Class.
When Armor Class and Attack Rolls get REALLY high, you don't always get to break it down like this. Eventually, enemies won't miss you because you were moving. They still hit you when you're dodging. When an enemy is well out of your league, sometimes the only reason you didn't get hit is the skin of your teeth giving you that 1/20 chance to avoid a fatal blow. But at the very least, your enemy wasn't just swinging at the air when they rolled lower than your AC.