A finisher is a spell (usually a creature) that sits on the top of a deck's curve and acts as a way to win the game all by itself. Finishers tend to require significant resources to play, so finishers that do not guarantee an imminent, if not instantaneous, victory are viewed sceptically, at the least, by the tournament community.
By the same token, finishers that take an especially low commitment of resources are highly prized. A player who plays his finisher and does not secure a victory is said to have "fizzled" or "burned out". The act of coming back from such a failure takes luck and skill, so a strong and resilient finisher is a must for any deck that is highly reliant on its success.