A filament is a fine, thinly spun thread, fiber, or wire. Originally the term referred primarily to animal or vegetable structures, but with advances in technology it is frequently used to refer to human-made objects including filaments of incandescent light bulbs.
Filament, also known as monofilament, is also used in wigs  (http://www.wigsalon.com/whatismono.html) to aid in breathability of the base that the hair is attached too. In medicine  (http://www.medicalmonofilament.com/html/body_information.htm) it is used for testing purposes. However, it is most known for its use as fishing line called monofilament line.
In astronomy a filament is a strand of cool gas suspended over the photosphere by magnetic fields, which appears dark as seen against the disk of the Sun. It is also used to refer to any thread like structure in the astronomical universe.  (http://space.about.com/od/glossaries/g/filament.htm)
Contrary to fibres (or staple fibres) which are cut to a selected length, the word "filament" is used in the textile industry to designate an endless or continuous object, the length of which is only limited by the capacity of the spool whereon the filament is wound.
An electrical filament is used to convert electricity into heat and/or light and refers to elements made of some kind of wire. Filaments are commonly found in traditional light bulbs.
Thomas Alva Edison found that carbon made the best filament material for his incandescent light bulbs.
Today most incandescent light bulbs use tungsten filament, which is even better.  (http://inventors.about.com/library/inventors/bllight.htm)