How did paper money start?

An important step in the history of money was the evolution of paper currency. Goldsmiths - craftsmen who worked with gold - naturally kept very secure safes in which to store their gold. The practice grew up among the public of storing their gold with the goldsmith for safe-keeping. In return, the goldsmith would give the depositor a receipt promising to hand over the gold on demand. If the depositor wished to make a large purchase, he could go to the goldsmith, reclaimed his gold, and hand it over to the seller of the goods. Chances were that the seller wouldn't require the gold, but would carry it back to the goldsmith for safe-keeping. Clearly, if the people to be reliable, there was no need to go through the cumbersome and risky business of physically transferring the gold. The buyer need only transfer the goldsmith's receipt to the seller, who could accept it secure in the knowledge that the goldsmith would pay over the whenever it was needed. If the seller wished to buy a good from a third party who also knew the goldsmith to be reliable, this transaction too could be effected by passing the goldsmith's receipt from the buyer to the seller. The convenience of using these bits of paper instead of gold is obvious. Thus, when paper money first grew up it represented a promise to pay on demand so much gold, the promise being made first by goldsmith and later by banks; as long as these institutions were known to be reliable, such pieces of paper would be 'as good as gold'.

Source : An introduction to positive economics ( written by Richard G. Lipsey).