In ranked choice voting you would take you ballot and rank all candidates for office. So say you have 3 candidates for president. You rank them in order of preference. As they tally votes candidates that don't have enough votes to win have their votes reassigned to other candidates. Person A ranks obama 1, some fictional guy 2, and mccain 3. Person B ranks mccain 1, the fictional guy 2, and obama 3. When they tally the votes, since neither front runner has enough to win, their votes get assigned to the second choice on each ballot, meaning the fictional guy wins.
In ranked choice voting you can't afford to alienate large swaths of the population. You have to remain liked enough by everyone to be ranked 2nd or 3rd on the majority of ballots. Under this kind of system the extremist polarization politics of today is more of a liability than a benefit.