Examples of risk-free investment are long dated United States Government bondss. They are considered to be risk-free because the likelihood of the Government 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.