RSUs are a promise to deliver shares (or cash equivalent) once vesting is met. Unlike options, there's no exercise price and no exercise decision. When RSUs vest, the employee receives shares that are immediately taxed as ordinary income at fair market value.
RSUs are typical at late-stage private companies and public companies because they have value even when the share price is flat, there's no 'underwater option' problem. Some private companies use 'double-trigger RSUs' that vest only on both service AND a liquidity event (acquisition or IPO).