This question pops up here from time to time.

The first people who would really want to solve this problem were merchants. If you're a Greek merchant travelling to England to buy , say, treacle, how do you avoid carrying a lot of hard currency- gold or silver- with you? The obvious thing is to find a merchant in your area who's selling something Greek- like olive oil- to England, and so knows an English merchant with whom he does business. You pay him: for a fee he gives you a letter of credit (or bill of credit, sometimes just called a note) for that English merchant. When you land in London you look up that merchant, present your letter of credit. That merchant would likely discount that letter, not give you the whole value. How much he discounted it would depend on how much he trusted you, the Greek merchant...or he might refuse to accept the note at all, or refuse the note until he'd verified it. But you can see it would be very useful for everyone concerned: the Greek merchant makes some money, the English merchant makes some money, and the English merchant now has a credit in Greece and so can put that against the next purchase of olive oil instead of hauling gold or silver to Greece.

That English merchant might realize that he's in a very handy position. If the Greek is buying treacle that's going to be shipped to Greece, and he knows a treacle merchant in England, why go to England at all? Far easier to just write to the treacle merchant and place an order. But if the Greek merchant sent him , somehow, the money, how would he know the treacle merchant wouldn't just pocket it, and never send the treacle? And if he told the treacle merchant to first send the treacle and he'd pay him on arrival, how would the treacle merchant know that he'd actually do that? The solution is to find a third party to hold the money- that English merchant who already does business in Greece. He would offer a bill of exchange. And that English merchant would find it very, very handy, if there's a lot of this sort of transferring to be done, to actually maintain an office in Greece. He'd then be more sure that the letters of credit were genuine, and could make more money. And start to act like, well, a bank. There are , of course, many more complexities, here, but you get the idea.

Of course, notes were not limited to merchants. If the Greek merchant met someone in Athens who had a friend in London who had given him a note for 20 pounds, the Athenian could sell that note to the Greek merchant and the Greek merchant could simply show up at the friend's house and present the note for payment. And, likewise, if George Washington sent you letter and a note from Mt Vernon to build him a house in Berkeley Springs, and you needed to pay somebody for barrels of flour, you might do so with Washington's note. And that man might present it to Washington for payment, when he passed through Mt Vernon.

And yes, you can imagine that verification ( and also some trust!) would be important. Think about this for a bit, and you can understand why forgery was punishable by hanging in 18th. c England.

A good notion of 18th c. ( and probably earlier) business practices can be gotten from the entry for Book-keeping in the 1st ( 1768) edition of the Encyclopedia Britannica