‘Prometheus’ is the space ship in the movie Prometheus which, based on ancient star maps discovered on earth, travels to the distant moon LV-223 in hope of finding an alien intelligence (the ‘Engineers’) that may have created life on earth.
In Prometheus, the crew discovers what appears to be a scientific or military installation belonging to the Engineers, with almost all of the inhabitants long since killed by creatures created by their own experiments with a black oily substance. Of the Prometheus crew
only one human (Elizabeth Shaw) and one android (David) survive. They take control of an Engineer ship, and set course for what they believe to be the Engineer home world.
(Wikipedia covers this quite well.)
In Alien: Covenant, the colonisation ship ‘Covenant’ lands on this same world, and the crew encounter David. Eventually, it’s revealed that
David released the black substance on the planet’s Engineer population before landing the ship, killing them all. He then spent years performing genetic experiments, including on Elizabeth Shaw, which culminated in his creation of what look very much like facehuggers, and subsequently a fully-grown alien, from the original Alien movie.
(Wikipedia covers this quite nicely too.)