Martial arts is the collective name given to a variety of hand-to-hand fighting styles, or fighting styles that involve weapons that are used as an extension of the body. Most fighting styles are unique to a particular culture, such as Karate to Japan, and TaeKwonDo to Korea. While many have roots in the period BC, there are variations of the styles that evolved in the last 200 years.
Interestingly enough, Karate is more of an anti-martial art, designed to help common folk prepare to fight against martial rule, during a time of weapons bans. Kara te do means "empty hand way" referencing this style without weapons. TaeKwonDo means "the way of the hands and feet".
Most martial arts were originally intended to be used for serious fighting, but in the modern age they are mainly practised as sports, with strictly codified rules; indeed some, such as Judo, were developed from other martial arts purely for sporting purposes. Many people, especially women, also learn martial arts for self-defense.