The 22nd Amendment to the U.S. Constitution prohibits any U.S. president from being elected to more than two terms and prohibits any vice president who rises to the office of president and holds the office for more than two years from being elected to more than one full term.
Both George Washington and Thomas Jefferson decided not to run for a third term as president. Historians say this indicates that the founding fathers implied that U.S. presidents should limit themselves to two terms. As a result, almost all presidents prior to the passing of the 22nd Amendment self-imposed a two-term limit on themselves. Only Ulysses S. Grant, Grover Cleveland, and Woodrow Wilson ran for a third term (all lost). Theodore Roosevelt became president after William McKinley's assassination and he tried to run for a second term (he also lost).
Franklin D. Roosevelt is the only president to serve more than two terms (he was elected to four terms, but died during his fourth term). It's believed that Roosevelt's long run was because the American people didn't want to change leadership during World War II. But almost immediately following Roosevelt's death, the 22nd Amendment was introduced and ratified.
Since then, many Congresspersons have introduced symbolic bills to eliminate the 22nd Amendment, but these are never taken seriously. As of this writing, 22 such bills have been introduced in the last 20 years alone, under every president since Ronald Reagan (including Barack Obama). But not one of these bills has been brought to a vote. They're considered a nod to the current president by his congressional supporters, and nothing more.
Nearly everyone who participates in the political process believes that the 22nd Amendment is important. It gives the American people more opportunity for choice in their leadership; it prevents one person from becoming some sort of monarch or dictator.