From the box of the game:
Ever since you left that last planet, you've been bothered by eerie sounds coming from somewhere in the hull of Nostromo, your giant transport cruiser. After setting the ship's controls on autopilot, you descend to have a look.
Yow! Every hallway in the entire maze-like hull has been lined with the grotesque eggs of some gruesome space creature. Quickly you sprint down the corridor crushing the eggs as you go. Then you see it! A hideous being with jaws like a beartrap. You run away from this brutal beast, not wishing to end up as an intergalactic snack. You turn a corner and stare unbelievingly. Another alien is just ahead.
Your job is to run through the hallways of your space ship and crush all the Alien Eggs that have been placed there. You must also avoid or destroy the adult Aliens and snatch up as many prizes as possible. Don't bother calling for help. Remember in space no one can hear you scream.