IBANs facilitate cross border payments (in particular) by having a common way to identify the country, bank, branch and account number of the beneficiary without having to know anything about the local clearing system. For example in the UK you need to know the 6 digit branch sort code, in Australia it’s the BSB, in the US it’s the ABA. But until the latter 2 countries join IBAN, you’re still going to need to know the local clearing codes. But if you want to pay someone in Mauritania or France, all you need is the beneficiary’s IBAN.
IBANs can also facilitate local payments, by ensuring beneficiary account numbers are in a machine readable format and they are protected against error by the strong check digit algorithm.