Abbreviation of Big Freakin' Sword (and it's less polite wording). Insanely big and heavy swords which sometimes weigh more than the character himself/herself. Generally they're also magical.
Something of a staple of manga, anime and other forms of Japanese popular entertainment, these impractical-looking but often deadly weapons are quite a common sight.
Despite their ludicrous size and weight, most wielders of a BFS can swing their swords without much more than mild inconvenience.