What is Martial Art? The arts of war, of fighting. Methods of incapacitating another human, developed recently, or over thousands of years. The fight as opposed to the flight. Rather than thinking of this as simply the kicking, punching foreign fighting styles, include in the category shooting, fencing, boxing, modern military training methods, and even ancient ones.
These all have a reason for existing, but I would say that a core tenet is discipline. These are all about developing control of your body to achieve an objective. These are all dangerous skills to have, so any teaching system involving these arts will also teach restraint, and honor and the like, mindsets that prevent one from incapacitating, say, every human one comes across.
The blurred line between competitive sports, to civilians able to defend themselves, to a militia, to an official army is the purpose for the existence of martial arts. The meaning has to be the culture and the feel of the art, the personal effect on you and the challenges you face learning it.