Respawn means, that when you die, you return after a set time, to be able to play once again, though most time it comes with some form of punishment (lesser level, lesser resources), but makes the act of dying more forgiveable. Respawning only occurs in the Xel'Naga Artifact Mode, after a 1-minute delay after death
However, in the Star Battle Classic or Vespene Control Modes, there is NO respawn, thus meaning that once you died, the game is over for you (except if there is an uncontrolled capital ship you can take over). That means that you should play carefully and avoid death whenever possible, as death is final for you in a game of Star Battle.
For more information about how to exactly avoid death, please refer to the strategy page.