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.)