A company can attract employees and incentivise existing employees in numerous ways. Giving employees equity in the company is a popular way for startups and fast-growing companies to reward their key employees for their performance.
A Share Vesting Agreement grants shares to the employee, but these shares are subject to a repurchase option so if the employee leaves the company or is dismissed then the company can buy back the shares for the nominal value of the shares. The shares are released from the repurchase option over a period of time, and this document governs how and when the shares are fully released to the employee and what happens to the shares if the employee leaves the company.
An Option to Purchase Shares is an offer from a company to an employee that they may purchase a pre-determined number of shares in that company at a pre-determined price. It operates as a type of security that gives the holder the option, but not the obligation, to buy the shares at this particular price. If the value of the shares has increased in the meantime (which is usual in a growing company) then the employee can make a substantial gain if they exercise the option.