A restricted stock award is when a startup grants someone stock as equity compensation. The award is "restricted" usually in the sense that it has a vesting schedule and is subject to repurchase if the recipient leaves the company, and that the recipient cannot freely transfer the shares to third parties. Restricted stock awards are much less commonly used as equity compensation than are stock options, as the associated tax burden is usually undesirable.
Note that restricted stock awards are often confused with restricted stock units (RSUs), but the two are distinct.