The interest rate which it is assumed can be obtained by investing in financial instruments with no risk.
Examples of risk free investment are long dated US Government bonds. They are considered to be risk free because the likelihood of the Goverment defaulting is extremely low.
The risk free interest rate is of significant importance to financial calculations such as use of the Black-Scholes formula for pricing stock options. 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.