After watching both Prometheus and Alien: Covenant (links to IMDb pages), the answer appears to be a combination of factors (WARNING: Spoilers for both movies follow, but as they are the entire substance of the answer, they are not wrapped in spoiler tags):
- The black "goo" containing some type of parasitic life form created by the Engineers for whatever unknown reason with the apparent intention of destroying life. (Prometheus)
- Additional experimentation and genetic engineering performed by the android, David (Alien: Covenant).
An article from The Verge (#1 in References below) does a good job of describing this latter piece of the puzzle in the following quote:
Michael Fassbender’s android David (he’s definitely the same character from Prometheus in this scene, as he’s called David by name) walks Billy Crudup’s character through his personal workshop of biological terrors. He shows off different mutations of the creatures, explaining that he has been trying to understand the aliens that were discovered in Prometheus, going so far as to genetically engineer new versions — a process that’s been waiting for one final puzzle piece to complete.
As for the former, the following quote from Hollywood Reporter (#2 in References below) doesn't provide a lot of additional insight:
Little is known about the parasitic life forms the Engineers created, but most of the creatures are connected to a mysterious black goo. Many different species who want nothing more than to infect another biological life form live in the goo, but the goo itself is also able to cause mutations.
I haven't read, seen, or listened to any of the extra-cinematic works associated with this franchise, so I can't really provide anything more substantial myself. However, this little bit of info does help to explain the rapidly evolving nature of the xenomorph, especially when coupled with another quote from the same article:
David, an android with mysterious motivations, inexplicably infects shipmate Charlie (Logan Marshall-Green) with a small drop of the black goo in his drink (it seems David, an artificial creation, has an interest in becoming a creator himself). After Charlie makes love to his wife Elizabeth, he unknowingly passes on an infection of a squid-like alien. In a horrifically memorable scene, Elizabeth is forced to have an automated Cesarean section to remove it (without anesthesia). Later in the film, a squid alien (officially known as a Trilobite) has grown considerably larger than the Engineer it captures, and ends up parasitically infecting the Engineer as well. In the closing moments of the film, we see a new alien burst from the Engineer's chest. The surprise is, this alien, spawned from a single drop of black goo, cross-infected by two human hosts, a squid alien and an Engineer, looks more like the Alien Xenomorphs that we're already familiar with from the Alien franchise.
There are likely other (more) useful resources out there, but these are a couple of things I found when I was trying to make the connection myself.
- The Verge - Alien: Covenant changes everything we know about cinema’s most terrifying monster (11 March 2017)
- The Hollywood Reporter - 'Alien: Covenant' — What You Need to Know Before Seeing the Prequel (18 May 2017)