Martial Arts is a term that in its pure definition is used to describe a codified system of fighting and training. This term incorporates both unarmed and armed fighting systems of all nations but common usage it is used to describe the unarmed martial arts of the Asia. The term originated in Europe during the 16th century and refers to the Arts of Mars (the God of War).
Martial arts seek to teach an effective way of fighting that one would use in a real situation should the need arise. Individual martial arts can be more or less effective in some situation when compared to others (eg. an unarmoured karateka, is at a significant disadvantage when faced by a pole axe wielding knight in plate armour).
Examples include various traditional karate styles, kenjutsu, ju-jitsu, various style of kung fu, savate, pugilism, etc.
There is a difference between these and martial sports, which might be defined as an activity loosely based on a martial art, but lacks a number of important elements. These elements might include a competitive basis, limited target areas, restriction of blows and/or the inclusion of blows that are not effective in an actual combat situation.