A method for stabilizing the value
of a national currency
against multiple freely-traded other currencies.
Some countries have very little interest in floating their national currencies on the open market, often because of the specter of high inflation in their past. One method of controlling this is to tie the value of your national currency to another country's strong currency, as was seen recently in Argentina with the peso's value tied to the U.S. dollar. However, this can cause problems when the currency to which yours is tied becomes extremely strong; Argentinian exports became uncompetitive because they had to be paid for in USD (or USD-equivalent) as the dollar kept rising against other world currencies like the euro, yen, and pound sterling.
The "currency basket" attempts to temper this effect by fixing the value of a currency to a theoretical currency built on percentages of other freely-traded currencies. For example, if Elbonia decided to fix the Elbo to a currency basket made up of 50% euros and 50% dollars, this would immunize Elbonian companies against dollar-vs.-euro fluctuation: should the dollar weaken against the euro, an Elbonian company's foreign bills payable in EUR would become more expensive (it would take more Elbos to buy the same number of euros), but bills payable in USD would become cheaper at the same rate (less Elbos to buy the same USD). A currency basket is often set by the percentages of a country's foreign trade made in each currency used, attempting to create just such a balance.
For example, let's take a look at Israel's currency basket (http://www.bankisrael.gov.il/deptdata/mth/curbaske.htm). The value of the new Israeli shekel (NIS) is a certain percentage of the total value of the basket. Meanwhile, as foreign trade fluctuates, the amount of each currency included is adjusted per year. In 2000, the basket consisted of US$0.6698, UK£0.0453, ¥7.2411, and €0.2493 (pre-euro, both the French franc and Deutschmark were part of the basket).
A quick Google search indicates that some other countries using a currency basket include Hungary, Slovakia, and Iceland.