At its most basic, "tagging" is the act of writing your name on a wall, on a newspaper stand, on a lamp post, or, let’s be honest, anything else that doesn’t belong to you.
The medium doesn’t particularly matter: marker or spray paint will do. In a pinch, and on the right surface, maybe even a ballpoint pen. The point is to put your mark where it wasn’t before, and to put it in a place where other people will see it.
And, like everything else in graffiti, the most important point is to do it with style.