Repurchase rights are contractual rights of the company to buy back shares from holders under defined conditions. Most commonly applied to unvested shares from departing employees, the price is typically the original purchase price for unvested shares and sometimes fair market value for other triggers, used to enforce the structural protections built into vesting and transfer restrictions. It is the structural mechanism that makes vesting meaningful at companies issuing actual shares (restricted stock, founders stock) rather than options.
The two main types of repurchase rights:
Vesting repurchase rights (the core mechanism for restricted stock):