Cut scenes are a narrative device in which the game pauses play to deliver a short cinematic sequence. They are usually animated, although occasionally filmed.
The best use of cut scenes is those which are relevant to play, such as setting up a task to complete. The Grand Theft Auto games are an excellent example of using cut scenes to convey information, and they carry the sense of a story with them.
The worst use of cut scenes are those which try to tell a story at the player. Overly long and full of writing that tries to telegraph emotion to a player, they misunderstand the relationship between player and game. Videogames are not a storytelling medium.