A chess-playing program (or a free-standing chess machine). The most well-known ones are Fritz and ChessMaster. They are banned from use on chess.com during play (and trying to use one is likely to get you banned) - except in very specific circumstances: a tournament created for this particular purpose, where all participants are aware that engines are being used. Such games should probably also be unrated.
Since a chess engine allows you to feed in a game position, and it will then calculate the best moves from that position, there can be no argument that it is clearly cheating to use them during play.
They are frequently used to analyse a game, after it has been completed.
What chess engines?