Theory
An outpost is a square, usually in the centre or just past it, that can never be challenged by an enemy pawn. A knight planted there is effectively immune to being kicked away, and knights in particular gain enormous value from a stable, central outpost — far more than a bishop does, since a knight’s short range means it depends on being close to the action.
Fighting for an outpost is really a fight over pawn structure: you need to either provoke or force the enemy pawn that could challenge the square to move elsewhere or disappear. This is why so much positional maneuvering in the middlegame is really outpost preparation in disguise.
Model Games
Petrosian’s games are the textbook reference for outpost play — he was famous for spending several quiet moves provoking exactly the pawn trade that handed him a permanent outpost, then never letting go of the resulting advantage.
Practice Positions
From a symmetrical structure, identify which central square is a potential outpost for each side and calculate the exact pawn trade or push needed to secure it. The move that provokes the trade is usually more important than the move that occupies the square.