The gold standard
This led to the birth of the gold standard. Back then, the banknotes themselves didn't hold any intrinsic value, such as gold and silver coins do. Instead, paper money was backed by precious metals (such as gold and silver), stored in a treasury vault somewhere, such as Fort Knox. The banknotes represented the right to collect those precious metals from a bank. This was more convenient than taking a wheelbarrow of gold bullion to the post office to pay the mortgage!
This was the case until 1944. At the end of World War II, yet another related system was introduced under the Bretton Woods agreement, which was the gold exchange standard. This meant that many countries fixed their national currencies' exchange rates to the US dollar, which was, in turn, convertible to gold, at a fixed rate. This system can be better illustrated by the following diagram:
Not only that, but this convertibility was no longer available to individuals or companies, but only to central banks. However, the Bretton Woods system ended in 1971, when the US dollar convertibility to gold was terminated. Since then, paper money has no longer been backed by gold (or anything else tangible), but just faith!