Why would be an explanation that I don't feel qualified to answer, but I can tell you that substances will react to form more stable states with less potential energy. Maybe someone else on this forum can shed a little more light on this for you.
As for balancing your equation, it should read C7H6O3 (Salicylic acid) + C4H6O3 (Ethanoic anhydride) => C9H8O4 (Aspirin) + C2H4O2 (Acetic acid). I remember doing this is in a Chem I lab. All you really have to know to answer your initial question is that everything reacts in a 1:1 mole ratio, then you can just use conversion factors.