Both in D&D 3.5 and Pathfinder, Spell-Like Abilities are described as having "no verbal, somatic, focus, or material components." In both systems, however, activating them as a standard action provokes attacks of opportunity.
Is any explanation given for this? If the activation of the ability is purely mental, what provokes the attack? How is this different from quickened spells, which do not?
Well, the difference between a quickened spell and a spell-like ability is that the quickened spell is faster; it is a swift action while a spell-like ability still requires a standard action.
The real reason is to have a mechanic to allow whatever kind of monster or whatnot to "cast a spell" even if it doesn't have a mouth or limbs or spell component pouch. Though it doesn't technically require a V or S or M, there's some kind of "concentrate for a couple seconds" activity that, while not quite counting as a somatic component, is still incompatible with jumping around in melee and therefore both provokes and is disruptable.
Similarly, Still Spell'ed spells don't have overt somatic components but still provoke. (As do silent, stilled spells without material components. And psionics in 3.5, for that matter.)
They provoke because while you are thinking/concentrating trying to activate the ability you are not 100% blocking incoming strikes from your opponent. Remember combat is fluid, your opponent does not stand there during your turn.
They provoke AoOs solely for balance reasons. Some races/classes do not get them, and exposing yourself to AoOs as a result of using them means that there is a risk of relying solely on those as opposed to your other class/race-based abilities.
Most of the time, spell like abilities are based on the HD of the core creature, and quite often have no limit. The actual spell requirements (V/S/M) are very specific. A creature doesn't have to eat a Fire Flower to spit Fireballs, they don't have to say Petrificus to use a Stone Gaze, and they don't have to flash gang signs with their hands to start glowing. Any of the above are just flavor. But what they do have to do, as mudbunny said, is dedicate a decent part of their action to the cause, which can become the entire turn of the critter and by time taken on the whole (appx. 6 seconds to the round) leaves the opening nice and wide open for interruption.
