Set in 2104, almost eleven years after the events of Prometheus and eighteen years before Alien, the film sees the starship Covenant sent to colonise a distant, habitable planet that the Weyland-Yutani Company has discovered. Upon arrival, the landing party is infected by some kind of spore and mayhem results. The Engineer starship from Prometheus is soon found on the planet and it is confirmed that the android David and Noomi Rapace's character of Elizabeth Shaw will both return from the earlier movie.
Hazarding a guess, I'd say that David and Shaw reached the Engineer homeworld and discovered it had been wiped out by the "black goo" genetic engineering experiments run amok. David and Shaw sent out a distress call that the Company received, resulting in them sending a rescue mission under the cover of being a colonisation expedition. I suspect the real mission will be known only to Walter, the David-type android on the Covenant, and maybe the captain.
The movie appears to have deviated from the original plan. Ridley Scott's original Prometheus II concept would have picked up shortly after the events of Prometheus and followed David and Shaw to the Engineer homeworld, with a later film more directly linking to the events of Alien. My guess is that 20th Century Fox decided to skip that movie and what we're seeing with Covenant is more the plot of the originally-planned third film. The fact that the familiar xenomorph is in this movie (along with a spine-shredding variant known as the "neomorph") adds to that possibility.
If this movie does well, there would appear to be scope for one more prequel movie (leading directly into the events of Alien, explaining what that Engineer ship was doing on LV-426) and then presumably we'd get Neil Blomkamp's Alien 5 project, which has been put on hold whilst Ridley Scott does his thing.