The X-Files is one of the divisions in the FBI, devoted to unsolved cases that appear to have some unexplained, paranormal elements. The files take their name from the filing cabinet where they were kept - originally filed under U for unsolved, they grew too big for the drawer and were moved to the less populated X cabinet. Soon, the X-Files became a dumping ground for reporting of UFOs, alien abductions, and other arcana that the FBI didn't want to investigate or didn't believe in.
Fox Mulder, a serial-killer specialist and a believer in paranormal phenomena ever since, as a child, he witnessed the abduction of his younger sister, requested to be transfered to the forgotten basement and began to ruffle a few feathers in the Bureau. Eventually, he was assigned a partner - the skeptical and scientific Dana Scully, who was assigned to discredit Mulder's works.
Instead of discrediting him, however, Scully slowly became Mulder's ally. The pair began to investigate cases that no one else wanted to touch and that couldn't be solved.