Listen server
A game server running inside one player's client, so the host both plays and referees.
The term comes from the Half-Life and Quake lineage, where the same executable could start a server and then join it. The alternative is the dedicated server: a separate, headless process on a machine in a data centre. A listen server costs the publisher nothing, since players supply the hardware and the bandwidth.
The price is host advantage. The host has zero latency to the server and sees every shot land instantly, while everyone else plays with delay and lives at the mercy of the host's upload speed. When the host quits the match ends — unless the game supports host migration. That is why competitive games almost always run on dedicated servers, while co-op and smaller titles make do with listen servers.