Many voting methods operate by going through several rounds. The usual way to interpret "multiple-round" is that several elections are held, with fewer candidates advancing from one election to the next, until a winner is decided in the final round. However, this article will also cover systems that have automatic or instant rounds (i.e. one election's ballots are used to simulate several rounds). Elimination-based methods generally are multiple-round. Runoffs are a common format for multiple-round methods.
Venice historically used a multiple-round method to elect their leader, which combined randomness and a form of Score voting.
One criticism of these methods is that they can incentivize voters to strategically vote based on who they think can survive elimination and win the final round.
Note that sequential multi-winner voting methods can be considered multiple round voting methods; not all of these methods involve elimination (e.g. Cardinal PR methods).