In a chess puzzle, you make the best move. This is the move that gives you the greatest advantage. In certain puzzles, like when you have to defend, every other move besides the solution will give a smaller chance of winning, by say, losing a pawn, only winning a pawn instead of a rook, or even getting checkmated! Basically, in a puzzle, incorrect moves are moves that aren't the best you can possibly make.
How do chess puzzles work?

ChessDude gave a great answer. I’ll just add that they are usually predicated on *forcing* moves. If the opponent has a totally open set of options, you can’t just assume that he’ll fall into a trap or that he’ll make a bad move. Just because you offer a rook sacrifice doesn’t mean he’ll give his queen to get it. Only if that’s the only way to stave off a checkmate.

true. they usually force something
I don’t understand the objective. Why are certain moves “incorrect”?