As Presdident, you are the leader of the group. You should preside at meetings and coordinate the activities of all committees. (Which is not to say you should run each one yourself.)You are also the primary liaison with the school, i.e., the principal, and usually external groups as well.
Like any other board member or volunteer, you can pitch in on specific projects as needed or as your workload allows.
Somehow I don't think you'll find yourself at a loss for things to do. It sounds like you are moving in exactly the right direction.
This year as president I have done everything from chair several committees that did not have chairs to run all of the "business" of the PTO. I have a co-president who currently is not involved. There is no vice-president. The secretary only does PTO meeting minutes and the Treasurer handles all of the finances and has pitched in to help me where there were needs. Next year, as I stated in other posts, I am trying to change the board to incorporate 1 president, 2 vice presidents (one to oversee fundraising and the other to oversee services we provide), a secretary and a treasurer. We also have committee heads (16 of them). The treasurer will handle anything related to funds, and the secretary will do all recording and correspondance. So, my question is, once I have delegated the overseeing of the committees to each respective VP what is the role of the president??? I know there is "business" that needs to be done....what else specifically is involved in that role?