Can anyone explain to me what is a chess engine? Thank you.

A chess engine is a computer program that can play the game of chess.  http://en.wikipedia.org/wiki/Chess_computer  Any chess-playing program that you buy (or download) e.g. ChessMaster is technically a chess engine.

When people talk about CHESS ENGINES on chess.com, they are almost always talking specifically about playing THE SAME GAME of chess against a human opponent AND AGAINST A COMPUTER (chess engine) at the same time - WHICH IS CHEATING. Essentially, you feed you human opponent's move into the chess engine, then you take its reply and feed that back to your human opponent.