It wont happen right away, but white aims to wins pawns (or material in general). Often happens in conjunction with infiltration of pieces into blacks queenside. The extra space + force means the pawns will be too weak to defend (so black relies on kingside counterplay).
So yes, there will be outposts, and yes, you'll probably get a passed pawn at some point, but even more basic, you're just wanting to win material :)
So how does white usually achieve this?
Just speaking very generally.
White plays a pawn break. So the move c5 for example. Or if black has played c6 the move b5 may be the main break.
After some pawn trades, white gets 1 or more open files. Then there will always be some kind of target. For example the d6 pawn when there's no pawn on c7. Or black's a pawn when there's no b pawn.
This might seem very minor... and in many positions it is minor. But the nature of a big space advantage is that you have more options to configure your pieces. So say you pile on d6 and they pile on the defense so you can't win it. Then you use your space to shift your attack to a7 (or to infiltrate onto different squares or even shift your attack to a different side of the board). The defenders can't respond because they don't have the room to redeploy as efficiently as you can.
Especially knights need room to dance around (and can be pretty effective at harassing weak pawns).
I have recently taken up the Bayonet Variation in the King's Indian :
My question to any experienced KID players is: what exactly is the aim of white's queenside counterplay? Is it to create a passed pawn? Or to just enjoy fine outposts for pieces? I'd appreciate it if someone could just outline white's main aims in his queenside play. Thanks!