Ranked ballots allow voters to choose multiple candidates, ranked in order of preference. It's easy as 1, 2, 3.
On election day all of the first choice votes are added up (just as we do with our current system). If someone wins 50% or more of the vote, they are declared the winner and the election is over. However, if no one receives more than 50%, the candidate with the least votes is eliminated from the race.
In a conventional runoff, a second round of voting would take place at this point and all the supporters of the eliminated candidate would vote for their second choice. With ranked ballots, there is no need for costly multi-round voting because voters have already marked their second choice. If your preferred candidate is eliminated from the race, your vote is automatically transferred to your second choice. Again, the votes are counted and if someone has a majority, they are declared the winner.
If not, another candidate eliminated and it repeats until there is a majority winner.