The FBI kept files on people for basically four reasons:
they were asked to by some other agency, e.g., as part of a security clearance investigation or because they were thinking of appointing them to some political position in the government
they were the victim of some kind of crime that involved a federal investigation (death threats, kidnappings, etc.)
they were suspected of some kind of federal crime themselves
they were considered possibly tied into movements that the Hoover-era FBI considered "subversive" — Communism, the USSR, Civil Rights, etc. — sometimes this happens just by association with other people who fall into these categories
Without looking at the files you can't really get a sense for which category or categories it falls into. I haven't seen Warhol's file and it isn't free online, but I've read a lot of FBI files (mostly scientists in the Cold War; I have a collection of such files). This summary of Warhol's file seems plausible — he was under suspicion of a federal crime, namely distributing "obscene material" across state lines. (The "across state lines" is a common way for something to go from a state crime to a federal crime in the USA.) Basically they heard Warhol was shooting a dirty film and wanted to see if it was indeed dirty enough to (in the 1960s) warrant prosecution. (I am not an expert in the history of pornography in the United States, but my understanding is that until the 1970s it was commonly prosecuted as "obscenity.")
The FBI appears to have concluded it was not obscene enough to warrant involvement/prosecution; the fact that the film in question won artistic awards probably didn't help with that (hard to argue it lacks artistic integrity).
Warhol's file seems to be about 80 pages long. That is pretty short for an FBI file, though not the shortest I have seen. Carl Sagan's is ~30 pages long. Nikola Tesla's was 350 pages long; Edward Teller's was 300 pages long; Richard Feynman's was 360 pages. The file trying to determine whether the song "Louie Louie" had obscene lyrics was 119 pages long. Albert Einstein's file is around 2,000 pages long. A hundred-ish pages sounds like a lot but most of the files are full of repetition, routing forms, etc., so it adds up pretty quickly. The 300-ish pages ones are the more typical — that's about the average length for something that is involving vetting of some kind. Einstein's is indicative of a serious, long-term investigation (J. Robert Oppenheimer's is something like that, too).