Say there are four candidates in a race. Everyone votes in a four-way election, but no one gets a majority. So the candidate in last place gets kicked out, and everyone votes again in a three-way election. If there's still no majority, then the third-place candidate gets kicked out, and there's a final election between the top two candidates. IRV does all that automatically in one election.
Voters rank their candidates in order of preference.
The counting process automatically simulates the runoffs. It provides the same result as if everyone kept coming back for runoffs. Since 1981 Austin has held 13 municipal elections, twelve if which have required a runoff with voters making an additional trip to the polls. IRV would offer significant savings of taxpayers' money and time. Since 1981 Austin has held 13 municipal elections since 1981.