A sublimated holdover from “old school play.”
There are no actual minimum ability scores in Pathfinder/D&D 3.x. There is nothing akin to First Edition AD&D’s requirement that you have a Charisma of 17 to become a Paladin, or a Strength of 15, Wisdom of 15, Dexterity of 15, and Constitution of 11 to become a monk.
BUT… minimum ability scores are still there, if you look hard enough. It is still true that you must roll high — from an optimizing standpoint — in order for certain Pathfinder classes to be viable.
The reason boils down to how some some classes rely on a single high ability score (“SAD” – Single Ability Dependent, like Fighters and Wizards), while others rely on more than one (“MAD” – Multiple Ability Dependent, like Paladins and Monks).
So, imagine you roll your scores and get the following array:
16, 13, 12, 12, 10, and 8
Well, you would make a strong fighter — if you chose to be a Human, you could bump your Strength up to 18. However, you would be a far-from-effective Monk — even if you were to assign your 16 roll to Strength, the highest your 1st-level (medium-sized) monk’s Armor Class could be would be a measly 14 (before factoring in feats). As a paladin, you would have either a low Strength stat or a low Charisma (needed for smite evil, channeling energy, and spellcasting).
So… it is still true, even in the player-empowering world of Pathfinder/D&D 3.5, that some classes are hard to “qualify” for, just as in First Edition AD&D. In fact, among the core 11 classes the Paladin and the Monk — the hardest to qualify for in First Edition AD&D — remain the hardest to roll good scores for. You can still play those classes, but you can’t necessarily be a powerful example of that class.
So, to optimizing power gamers at least, Pathfinder/D&D 3.5 still makes certain classes less attainable, while still technically allowing you to choose any class you want… A nice balance, if you ask me.