A banknote is a promissory note issued by a bank, which originally guaranteed the bearer payment upon demand in a more tangible type of currency. Modern banknotes (or paper money) are not generally redeemable, but are instead treated as if they hold value in their own right.

Benefits

Banknotes are cheaper to produce than coins, as well as being easier to transport. Unlike coins, which lose value as they wear away through use, a paper bill retains its entire worth when damaged.

Drawbacks

It is considerably easier to counterfeit a paper bill than it is to forge coins. Banknotes in and of themselves only have agreed-upon value, while the worth of precious metals is much more physical.

History

Banknotes originated in ancient China, arising as an answer to the inconveniences of transporting large quantities of coins. European banks first began issuing notes in the 1500s.

Issuing

Banknotes were often issued by private banks in the past, but nearly all modern paper currency is produced by government-controlled central banks. Since 1935, all banknotes in the United States are printed by the Federal Reserve.

Convertibility

Most modern notes are not directly convertible--capable of being exchanged for precious metals. Some banknotes are convertible for bonds of the bank's assets rather than gold or silver, but many cannot be exchanged for anything at all. This has the drawback of increasing the risk of inflation.

Source:

Wise Geek: What is a Banknote?