The spawn is the area where players appear at the beginning of the round (if the game is round-based) or immediately after being killed (if it is not round-based.) "Spawn" is used in this sense almost exclusively in team-based games; most other games have "spawn points" scattered throughout the map.
"to spawn" (or to "respawn" in non-round-based games) refers to the act of appearing at the spawn or spawn point.