Article II of the U.S. Constitution outlines the powers that the President holds, but if you don't want to read the original document you can read a summary by the University of Cornell Law School.
The President is the Commander-in-Chief of the armed forces, and he/she can make treaties with the approval of the Senate. He/she is also responsible for nominating the heads of all of the Departments, which the Senate must approve as well. He/she can issue executive orders, which are similar to laws, except that they don't have to be approved by Congress.
The President can issue pardons for federal offenses, can convene Congress for special sessions, and of course, can issue a Presidential veto on legislation approved by Congress. However, there is a catch. The President cannot veto only certain parts of the legislation; instead, he/she must accept or reject the entire legislation. Also, a veto can be overridden by a two-thirds vote from Congress.
Finally, the President delivers the State of the Union address annually to both houses of Congress.