Compared to the Bank which it replaces, the Stock Exchange gives an extra +15% to the city it is built in.
At the risk of dramatic oversimplification - a stock exchange is an organization which allows "brokers" to buy and sell "stocks" and "bonds." A stock represents part ownership in a company, and a bond is a loan to a company, which the company guarantees to repay with interest. If the company does well, the investors make money; if the company does poorly (or fails entirely) the investors lose money.
The primary benefit of a stock exchange to society is that it allows companies to concentrate a large amount of wealth to accomplish something that no individual (or perhaps government) would be able to afford. In the nineteenth century, for example, construction of the United States' railroad network was in large part financed by individuals who purchased shares of railroad companies. Earlier in history, the great British and Dutch trading companies were similarly financed.
For a long period of history, the English city of London was the financial center of the world. The London Stock Exchange is one of the largest exchanges in the world, as well as one of the oldest. Though officially founded in 1801, it can trace its origins to the late seventeenth century, when - the brokers having been expelled from the Royal Exchange for rowdiness - buying and selling stocks took place in London coffee houses.