Domestically, the President can do the following things:
1. nominate certain federal officials;
2. remove certain officers;
3. pardon people who were convicted of federal (not state) crimes;
4. veto (and sign) legislation;
5. make Executive orders (sort of like laws, but no Congressional
approval is required; therefore, executive orders subordinate to any
conflicting law that was enacted by Congress).
Internationally, the President has the following powers:
1. enter Executive Agreements with other countries (these are similar
to laws, but since they don't require consent of Congress, they would
subordinate to any conflicting law that Congress enacted);
2. enter into and negotiate treaties (which require consent from 2/3 of the Senate, so they are superior to ordinary laws);
3. commander-in-chief of the armed forces.
For a more detailed list of the Executive's powers, consult Article 2 of the Constitution.