The Space Invaders are the unnamed alien threat that make up the antagonism of the iconic video-game franchise of the same name - they were never given a name or background in the original game but have nevertheless become one of the most iconic villains in any video-game franchise.
The Space Invaders are strange creatures that spawn out of nowhere and descend at ever alarming rates, the unnamed protagonist of the series must use a space-cannon to fire projectiles (presumably laser-beams) at the Space Invaders to destroy the alien "drones" before they can reach the bottom of the screen.
Presumably this represents the Space Invaders attempts to "land" or take-over the world - if they manage to do so the game ends (presumably meaning the Space Invaders succeed in their plan).
However the more Space Invaders one destroys the greater the rewards become, yet they also become ever harder to defeat as time goes on (if you wanted to stretch the imagination this could be considered the "advanced waves" coming in to deal with the troublesome cannon-welding "hero").
The Space Invaders can also fire back at the hero with their own beams of energy and attempt to destroy the cannon, again if they succeed it is a "Game Over".
Every now and then a mysterious large UFO arrives as a "bonus stage" and rewards extra points for defeat - this is presumably the mothership of the invasion fleet (and thus a greater loss to the aliens, hence the extra points for defeating it).
Ultimately the fate of the (game) world will be to fall to the Space Invaders as the player can never truly defeat them, as they will just keep coming until eventually they become too fast to stop - this can take a long time however.. to the point the "battle" could be played out (theoretically) indefinitely. More recent games, like Space Invaders Extreme, have averted this a little by creating different stages with huge bosses.