Well, it’s the Iron Bank’s reputation, but it’s not just the Iron Bank – it’s the whole economic might of Braavos. If you want access to their internal economy, which includes all the goods they’ve imported from across the world and all the goods they will export to the rest of the world, you’re going to need some Braavosi coins, so you’re willing to exchange gold for iron – especially when you know that the exchange works the other way too.
Where the Iron Bank comes in is that it’s got a lot of gold and other valuable stuff in its reserves, but it’s also issuing financial instruments that are denominating in Braavosi currency, so in a weird sense Braavos has an iron standard that is also partially backed by gold.