The Wikipedia definition of an "outpost" is this: “A position on the chess board where a knight is defended by a pawn from its same side.” Does it have to be a knight?
There is no "official" definition because there's no ISO standard for chess terminology, so the term means whatever the author wants it to mean, but I'd say the essence of it is that it is a "safe" and "advanced" square for a piece, where "advanced" typically means at least the 5th rank. As an analogy consider common non-chess definitions of outpost such as "an outlying or frontier settlement" or "a military base established in another country".
"A position on the chess board where a knight is defended by a pawn from its same side" is not only too restrictive by being limited to knights, but at the same time is too unrestricted because it would include something like a white knight on f3, which while protected, is hardly at an out-post; it's more of a "home base".
As for the "safe" part, it's a bit relative, but generally it means that it is not easy for the opponent to chase away or trade the piece. This may mean that the piece can't be chased away by pawns, because there are no pawns on the adjacent files or they are too far advanced, or because the pawn move to chase away the piece would come at a cost. Alternatively the opponent could trade it for a piece, but sometimes it's a bad tradeoff because the player who had the outpost might get some compensation such as a protected passed pawn. Or sometimes there is no way to trade it without sacrificing material, for example in a knight vs bishop scenario where the bishop is on the wrong color squares, so the only way to capture the knight is with a rook.
Finally, while not all outposts are for knights, perhaps most are; the reason for the emphasis on knights is due to knights being short-range pieces. Rooks and bishops can often be active from their home territory when on a good file or diagonal, but knights need to move closer to the action.
No, it does not have to be a knight.
It is really any forward square (5th rank or 6th rank), occupied by any piece (knight, bishop, rook, and more rarely since it can be chased away by less-valuable pieces, but even a queen sometimes). The piece usually applies uncomfortable influence over the opponent’s position.
For example, I have seen rooks planted often on d6, protected by a pawn (on e5 or c5, or even both). The rook exerts great pressure, but if taken, a strong passed pawn appears instead...trading one advantage for another.
It also really does not even have to be protected by a pawn, as long as it is, or can be, defended enough that you can continue to control it. A knight on e5 protected by a Re1 is a common example here.
P.S. GM Dofrman in the book, “The Method in Chess” has his own definition of an outpost: “an outpost is a square on a half-open file in front of an enemy pawn, situated on the 6th (for White - on the 3rd) rank.”
When I watched the videos on chess.24.com, even GM Jan Gustafsson seemed to be a little taken aback by his definition, thinking it should be more broad.
Personally, I think that his definition is a bit limiting.