Instant Runoff Voting, also known as Ranked Choice Voting, is a type of election where instead of voting for one candidate you rank any or all of the candidates in your order of preference. 

There is a system of rounds that is similar to simulating multiple elections. In the first round, everyone's vote goes to the candidate that they ranked first. If any of the candidates has a majority (>= 50% of the votes) then they win the election.

If none of the candidates have a majority then the candidate with the lowest number of votes is eliminated and the people who voted for that candidate will have their vote assigned to their next highest choice. This process repeats until one of the candidates has a majority.

It's like simulating multiple elections because we can deterministically say "if candidate A didn't run for election this person's vote would go to candidate B instead" and choose a candidate that the majority of the voters would be satisfied with.

In Ranked Choice Voting your vote always matters unless all of the candidates you voted for were eliminated before a majority was reached. That's why it's in your best interest to rank all of the candidates. 

Ranked Choice Voting also helps solve another problem which is when you have multiple candidates who have very similar platforms. Consider the following example:

There are two candidates, A and B, who want to make the phone policy at Stuyvesant more lenient while one of the candidates, candidate C, wants to make it more restrictive. 

Sixty percent of the school prefers the two candidates trying to make the phone policy more lenient and forty percent of the students would prefer the candidate who wants the phone policy to be more restrictive. 

The sixty-percent who prefer a more lenient phone policy would be fine with either candidate A or B, but a bit more than half of them prefer candidate A while the other prefers candidate B. 

All of the forty percent who want a more restrictive phone policy vote for candidate C.

In a plurality election the results would look like the following:

Candidate A: 31%

Candidate B: 29%

Candidate C: 40%

Even though the majority of the student body prefer candidates A and B candidate C won the race because candidates A and B cannibalized voters from each other.

Instant Runoff Voting solves this problem. If we assume the people who voted for candidate B wold have voted for candidate A if candidate B never ran then we can assume that they ranked candidate A as their second preference and candidate A would win the majority with 60% of the votes. It would more accurately reflect the desires of the student body. 

Here's a video explanation for further research.