"Foam Fighting," or on the grander scale, the sport of Medieval Combat Reenactment, is based around actual fighting with medieval weapons (normally, these weapons are made of safe materials, like foam, hence the name). Participants use medieval weapons (ie. swords, shields, spears, arrows, etc.) to maim, kill, and otherwise destroy the enemy fighters.
Some groups, like the SCA, are completely devoted to perfect historical accuracy, while others, like Amtgard, are very much based in fantasy, with semi-realistic rules regarding "Magic" (ie. throwing foam "Fireballs"). Most groups, like Dagorhir and Belegarth, M.C.S., however, are based entirely around the game of fighting, with the realism/fantasy aspects added in as secondary. The sport is very fast-paced, and everyone, including the physically handicapped, can play. (Some people are known to fight until they are 40+ years old.)
Hope that explains what the sport is for anyone who isn't familiar with it.