Tycho Nestoris: The Iron Bank dates from when Braavos was still "the Secret City", filled with runaways and refugees from the Valyrian slave lords. The first tradesmen to achieve success realised that if they pulled their resources, they could loan money to their less fortunate fellows and build a better Braavos. For a profit, of course.
First they needed a space to store their combined gold, safe from thieves and more importantly each other, for the business rivalries that created their fortunes were not easily put aside. They found an abandoned iron mine outside the city and sealed its only entrance with heavy gates and bars and set guards supplied by every principal investor. Each guard watched the gate, and the other guards. Over time, this distrust vanished as the investors gave up their other businesses and poured their energies into the new endeavour, now called the "Iron Bank" - after the mine. We have since moved to more spacious quarters, but they still keep their first vault, not merely to remind us of our roots, but because we did not become the world's greatest depository of wealth by wasting assets, no matter how minor.
If you are an aspiring merchant, you come to us to buy ships and goods. If you are an aspiring shopkeeper, you come to us to buy your shop. Whatever you need in this world, we are the conduit. Even a throne can be yours if you are an aspiring king, or stay yours if you are a sitting one. Just ask House Lannister of Westeros.
We are not the only bank in this world. Every Free City has its own. But when those banks need gold, the come to the Iron Bank. We lend to princes, kings, merchants and tradesmen. If a prince or king cannot pay us back, well... the world lacks for loyal men, not ambitious ones. We simply fund the rise of new princes and kings, and they tend to honor our investment. If a merchant refuses to repay us, well... the vicissitudes of trade are well known, and Braavos is full of men who... are... not. One way or another, the Iron Bank will have its due.
- Valyrian Freehold (indirectly mentioned)