Magic is a different concept in each game. Don't try to draw the explanation from a pre-existing one in your head, just let the game explain it to you and that's what it is. In this game, magic is the knowledge of the ancients flowing through you, and thus you can use it. In FF8, magic is the extraction of energy from a monster stored into a para-magic item that can be used just like any other item. ect. ect. It's different in every game.