In the game, you play as a tank, and shoot multiple aliens from above before they either shoot you or they reach the bottom of the screen. If the Aliens reach the bottom of the screen this counts as a successful invasion by the Aliens. Depending on which version you're playing this can either be an Instant game over regardless on how many lives you have left or it will only take away a life.
The maker of this game never revealed the name of the race or races of the aliens in the Space Invaders game. likewise, he never revealed which nation state your tank is fighting for. So these details were omitted from the plot by the game creator.