An underground film is a film essentiallyconceived and created by one person making a strong personal statement radically differing in form, technique and content. Usually made with meagre funds and mostly screened far outside the commercial movie channels.

The term originated in 1957 when American film critic Manny Farber used the term "Underground Films" first referring to directors who's "anti-art position" stood like a statement in Hollywood, such as the likes of Raoul Walsh (The Birth of a Nation) and Howard Hawks (Scarface). Later the term was used mostly to describe new independent filmmakers.

To explain what kind of films are underground some examples of movies that where considered radical deviations in terms of form, technique and content.

Chicken Hawk: The Men Who Love Boys (1994) - Adi Sideman
A documentary about members of the controversial NAMBLA group  (North American Man / Boy Love Association) Who discussing why their organization is supporting men and boys in need of sexual and/or emotional relationships. A traditionally structured documentary in form and technique, but the disturbing subject is radically offsetting content-wises, the average consumer of commercial cinema probably does not want or dares to engage this subject.

Mothlight (1963) - Stan Brakhage
A "found foliage" film composed of insects, leaves, and other detritus sandwiched between two strips of perforated tape, a radical twist.

Pink Flamingos (1972) - John Waters (photo)
Number 29in the famous '50s films to See Before You Die' list! Despite being a traditional structured comedy, considered an underground film. A transvestite (Divine) eating dog po is not considered that suitable for the commercial circuit.

Half-Cocked (1994) Suki Hawley
A traditional narrative film about a touring indie rock band. This film may be regarded as an more "indie"  than "underground"movie. However, the  the bands music is definitely not mainstream,  and therefore be categorized among underground films

Conclusion
A film that is essentially conceived and created by one person whereby he/she wants to make a personal statement and radically different in 'form', 'technique' or 'content', or all three of those in the broadest sense possible.