1. Creating an outpost
2. A famous outpost
A knight outpost is a square from which a knight cannot be evicted by either a pawn or another minor piece. Generally, knight outposts are not gifted by an opponent, but must be created.
In position 1, white has advanced his a-pawn to a5, thus securing c4 as an outpost for his knight. The knight cannot be dislodged from c4.
In position 2 (Karpov - Kasparov, 1984/5), Karpov declines to recapture the pawn on h4, temporarily sacrificing a pawn to get his knight to the outpost on f4 where it cannot be dislodged.