The knight on d5 below can never be driven away. Black has no pawn on the c-file and none on the e-file, so …c6 and …e6 are not available now and will not become available later, and no other black piece can trade it off without giving up something better.
7 
2 
g The two conditions
A square is an outpost when your pawn defends it and no enemy pawn can ever reach a square that attacks it. Both halves matter. A knight on d5 defended by the e4 pawn is only an outpost if Black’s c-pawn and e-pawn are gone or fixed somewhere they can never come; while Black still has a pawn on c7, …c6 kicks the knight and the square was only ever a resting place.
Rank matters too. On your own third or fourth rank a protected square is just a nice square. It becomes an outpost worth playing for on the fifth rank, and on the sixth it is close to winning on its own, which is where the old coaching line about a knight on d6 being worth a rook comes from. That is an exaggeration you should take seriously.
Why knights care and bishops do not
A knight is the slowest piece on the board and the only one that gains from having a permanent address. Sitting on d5 it hits b6, c7, e7, f6, f4, e3, c3 and b4, half of them in Black’s position, and Black has to arrange his pieces around it for the rest of the game. Compare the bishop on e7 in the diagram: it can be swapped, chased or simply blocked, and it does not need a hole to work from because the diagonals are already there for it.
That is one of the clearest cases where a knight beats a bishop: a fixed structure with a hole on the fifth rank.
Where outposts come from
From pawn trades, always. Every pawn that leaves the board stops guarding two squares, and those two squares never get guarded by a pawn again. Black’s missing c-pawn in the diagram is what created d5, and the pawn left behind on d6 is a matching weakness on the same file, which is a backward pawn staring up at a hole.
So the question to ask before any pawn move is not only what it attacks. It is which square it stops defending, and whether a knight would like to move in there.
Once you have a knight on an outpost, look for forks: from the fifth and sixth rank, an unshiftable knight is a forking machine.