The length of a single term for the President of the United States of America is four years. Presidents are allowed to serve up to two terms if re-elected by the people.
The rules behind how many terms a president should be allowed to serve was heavily debated as the Constitution was written. It was decided that if the president was to serve an additional term, he or she must be re-elected, and not simply appointed by legislature.
The number of terms a president should be allowed to serve was also debated, but it was decided that only allowing presidents to serve one term may result in not having the best person for the job.