These two films essentially define the sci-fi/horror genre. A race of incredibly lethal aliens stows away onboard a spaceship, resulting in a brutal struggle for survival. Only warrant officer Ellen Ripley makes it out alive. Oh, and Jones the cat.
Jones is the spaceship Nostromo's "ship's cat," and spends the movie hiding in various dark, dank corridors and occasionally jumping out and scaring the crew. In fact, Jones is responsible for what is probably the best-known, "Oh, it's just the cat" jump scare in horror history.
While Jones has some close encounters with the alien in the first film, it never attacks him directly. Ripley tucks Jones into her cryosleep chamber at the film's end. This gives Jones the distinction of most likely being the longest-lived pet in film history -- he and Ripley are in suspended animation for 57 years before being picked up by a salvage crew. They're both sent to a space station orbiting Earth, where Jones presumably lived out his days (Ripley soon left on another mission, and the length of her cryosleep certainly exceeded Jones' natural life span).
If you're really interested in the story of Jones the cat, you can even read about the events aboard the Nostromo from his point of view!