When you preside over something, you're acting as the leader or president. The captain of a club presides over the meetings.
Whether your title is President or not, when you preside, you're acting as a president or another kind of leader. A judge presides over a courtroom. The owner of a business presides over staff meetings. If you work in an office, your boss presides over the office. Presiding can mean ruling or just supervising something. If you preside over something, you're in charge of it.