The alien fetus was a fetus of an alien given to the Syndicate as part of their role in the colonization of Earth. In exchange for the fetus, members of the Syndicate sacrificed members of their own families, including Cassandra Spender and Samantha Mulder. Possession of the fetus provided the necessary alien DNA needed to begin creation of an alien/human hybrid.
Discovery in The Facility
Mulder and Scully first saw the fetus in 1994, during their early investigation into the Project. After Scully entered the secret facility that was supporting the Alien/Human hybrid project, she discovered an alien fetus within a small cryotube. The fetus she discovered must have been one saved for further testing by the conspiracy. (TXF: "The Erlenmeyer Flask")
In a featurette about "The Erlenmeyer Flask" from The X-Files Season 1 DVD, makeup artist Toby Lindala demonstrates the sculpted model used to film the alien fetus, referring to it as, "the little guy that Scully pulled from the liquid nitrogen." He then recalls, "We did a bunch of tests with putting the stuff in actual liquid nitrogen, pulled it out and it would frost over and steam. But unfortunately, it wasn't under hot studio lights. On the day, it came under the hot lights and there was a lot of stress on the piece and a lot of stress on me subsequently, because the thing started falling apart. I was frantically just gluing the ones back together. It had just got out of the shot before a big chunk of the head went," he laughs and indicates a far off direction while saying, "blasting out that direction."