It is an abbreviation for telling another person to fuck their own face. It stands for "F.uck Y.our F.ace." A person who is using this expression may state the letters as "F-Y-F" or pronounce it as one word as "fyf" which rhymes with the word "life."
F.Y.F. is derived from telling somebody "to take a step back and literally fuck your own face"
Justin: "You know Rob, you are a total douche bag!"
Rob: "Well you can go F.Y.F."
An angry and pissed off Tom Cruise would respond with: "Now I want you to take a step back... and literally fuck your face!"