Vesting is a term usually related to pension plans that some employer's provide to their employees.An employer may make contributions to the plan by matching the employee's contributions or set aside an amount based on a percentage of the employee's salary and their years of service, depending on how the plan is set up. An employee is considered "vested" in a pension plan, once they have earned the right to receive benefits from the plan upon retirement. This is based on a minimum time period of employment. When working for a company that offers a pension plan, the employee "vests" in the plan by fulfilling the employee's financial obligations and work requirements as defined by the plan.
Vesting can also refer to other employer provided benefits, such as stock options. Many employers provide employees the opportunity or "option" to purchase shares of the company's stock at a future date at a predetermined set price. To cash-in on the "option" or purchase the stock at the set price, the employee must usually remain employed by the company from the time the "option" is granted until the date that it can be exercised. At that time the employee is considered vested as defined by the terms of the stock option.
(For more on this read, The 401k and Qualified Plans: Introduction and Get the Most out of Employee Stock Options.)
This question was answered by Katie Adams.