In order to overturn a presidential veto, Congress must approve the returned bill by a two-thirds majority in both Houses. Once the bill receives this approval, it becomes a law. A bill that does not receive the required majority in both Houses does not become a law unless Congress presents it again to the President and he signs it into law.
While the U.S. Constitution does not include the word "veto," Article I, Section 7 states, "Every Bill which shall have passed the House of Representatives and the Senate, shall, before it becomes a Law, be presented to the President of the United States." This is the president's opportunity to veto the law. He has 10 days, excluding Sundays, to return the bill to its originating House of Congress, along with a statement of his objections. If the originating branch passes the bill by the required majority, it, along with the president's objections, go to the other House for consideration.
If Congress adjourns before the 10 day approval period is complete, eliminating the president's ability to return the signed bill, it does not become a law. This is called a "pocket veto," and the bill does not return to Congress after they reconvene.
According to About.com, Congress rarely overrides a presidential veto. Between the years of 1789 and 2004, the record shows 1484 regular presidential vetoes with Congress overriding 106.