Run-off election

A run-off voting system can refer to any kind of a voting system where the candidates at the bottom are excluded from the race, ensuring the winning candidate actually has a majority of supporters.

Two-round system
In the United States, a run-off election normally refers to an election based on the two-round system.

This system divides the election into two rounds. In the first round, all the candidates are running in the race, and, if nobody wins a majority, the two most popular candidates enter the second round, the winner of which wins the election.

Instant Run-Off Voting (a.k.a. Alternative Vote)
The instant run-off system, on the other hand, is a system of preferential voting, where voters choose their candidate in order of preference.

As a result, the unpopular candidates can excluded from the race one by one automatically, with their votes being redistributed according to the voters' next choices. The voters don't have to visit the polling stations the second time, and the system itself gives the smaller candidates better chances of winning.