Definitions for "Deathmatch"
A style of play that involves 2-16 players in a free-for-all situation. At the end of each round, the player with the most kills wins.
Known as DM for short, deathmatch is a pure combat multiplayer mode where it's everyone for themselves. Take out as many enemies as you can, and minimise the amount of times you die.
Every player for themself, basically. Score a point for each kill, and the player with the most kills at the end of the preset time limit is the winner. This is the core of most online gaming.