A Japanese slang term related to the Western concepts of "always wear clean underwear when you go out" and "fuck me heels", fighting panties are the racy, lacy undergarments that a woman wears when she goes out on the town with the intent of scoring that evening. The term brings to mind the idea that in the bars and nightclubs of the Far East, love is a battlefield, and all the other women are one's competition.
Probably the most notable use of the term was in the artist portrait that manga-ka Hiromu Arakawa drew for the first tankobon of Fullmetal Alchemist, in which the phrase was prominently displayed. Unfortunately, to Ms. Arakawa's chagrin, that image seems to be the one that they always use whenever someone writes an article about her...