It was an unwritten rule for over a century-and-a-half in American politics that no Constitutionally qualified citizen elected president would ever seek a third term.
Political folklore cites President George Washington as refusing to seek a third term for fear of the American president becoming what he fought so hard end — a monarchy ruling the American people.
It was in 1940 when the godfather of American Socialism, Franklin D. Roosevelt, broke with tradition and successfully won his third term to the White House. To rub his opponents collective noses in it, FDR ran for and won his fourth term in 1944.
Thankfully, the Twenty-second Amendment to the United States Constitution cleared the US Congress in 1947, and was ratified by the requisite number of states in 1951.
As the Twenty-second Amendment states; (emphasis mine)
No person shall be elected to the office of the President more than twice, and no person who has held the office of President, or acted as President, for more than two years of a term to which some other person was elected President shall be elected to the office of the President more than once. But this Article shall not apply to any person holding the office of President, when this Article was proposed by the Congress, and shall not prevent any person who may be holding the office of President, or acting as President, during the term within which this Article becomes operative from holding the office of President or acting as President during the remainder of such term.
So how could someone conceivably serve as president for ten years?
Example: On Jan. 20, 2019, President Trump would mark two-years exactly as president. If he were incapable of serving as president as of Jan. 21, 2019, that would be less than two-years that Vice President Mike Pence would serve the remainder of the term as his assuming the presidency.
Theoretically, because President Pence served as president for less than two-years, he could constitutionally be president for two more full terms.
However, if a theoretical President Pence served more than two-years (even two-years and a day) as president, he could only serve as the POTUS for one future term.
Yes, Democrats and RINOs have repeatedly attempted to dump the 22d Amendment.