Risk-free interest rate is the theoretical rate of return of an investment with no risk of financial loss. The risk-free rate represents the interest that an investor would expect from an absolutely risk-free investment over a given period of time.
Risk-free assets
Risk-free assets usually refer to short-dated government bonds. For USD investments, usually US Treasury bills are used, while a common choice for EUR investments are German government bills or Euribor rates. The mean real interest rate of US treasury bills during the 20th century was 0.9% p.a. (Corresponding figures for Germany are inapplicable due to hyperinflation during the 1920s.
These securities are considered to be relatively risk-free because the likelihood of these governments defaulting is perceived to be extremely low and because the short maturity of the bill protects the investor from interest-rate risk that is present in all fixed rate bonds (if interest rates go up soon after the bill is purchased, the investor will miss out on a fairly small amount of interest before the bill matures and can be reinvested at the new interest rate).
Since this interest rate can be obtained with no risk, it is implied that any additional risk taken by an investor should be rewarded with an interest rate higher than the risk-free rate (on an after-tax basis, which may be achieved with preferential tax treatment; some local government US bonds give below the risk-free rate).
Application
The risk-free interest rate is thus of significant importance to Modern Portfolio Theory in general, and is an important assumption for rational pricing. It is also a required input in financial calculations, such as the Black-Scholes formula for pricing stock options and the Sharpe Ratio. Note that some finance and economic theories assume that market participants can borrow at the risk free rate; in practice, of course, very few borrowers have access to finance at the risk free rate.
Why risk-free?
One explanation for the assumption that no default risk exists is due to the nature of government debt. For a fiat currency, the government retains the theoretical capacity to print as much of that currency as will be required to pay its own debts (in that currency). In this case, true default is theoretically impossible: owners of government debt can always be paid, but with money that may have substantially lower value. Rather than reflecting the default risk of the government, the risk-free interest rate, therefore, reflects the likelihood that the government will print money to pay its debts, thereby debasing the currency. Note that this does not apply to some currencies, such as the Euro,because no individual government of the Eurozone has the authority to print currency. Of course, many countries have other measures and institutions, such as theoretically independent central banks, to reduce the likelihood of such an occurrence.
An alternative interpretation is that, while no investment is truly free of risk, scenarios in which a major government with a long track record of stability defaults on its obligations are so far outside what is known that one cannot make quantitative statements about their chances of happening, and, therefore, it is simply not feasible to include them in financial planning. A German investor living circa 1904 trying to decide whether to purchase long-term bonds issued by the German government could scarcely have been able to anticipate a World War followed by hyperinflation.