During the Constitutional Convention in 1787, our Founding Fathers hammered out the rules for running a democratic government, and it wasn't at all easy. A lot of stuff was a compromise between all the disagreeing factions. On the question of how long a president should serve, some thought it should be for life, while others suggested a six, seven, ten, or even 12-year term with no re-election. Since no one could agree, the question was sent to the “Committee on Postponed Matters,” which sounds like a good committee to be on, especially for procrastinators. However, they did come up with the four-year term with re-election possible.
As far as presidents serving two terms, that was not in the original constitution. It became a custom, though, set by Washington and Jefferson, because presidents get really tired of the job after eight years. The few who did not found that the voters got tired of them after eight years. So why do representatives and senators get to run for re-election as long as they want? Read up on what the US Founding Fathers had in mind for these offices and how our system came to be the way it is at Mental Floss.