Vesting is a term used in both Defined Benefit and Defined Contribution Pension Plans. When an employee is fully vested, such employee is entitled to the full benefits of the plan. Vesting can be gradual, or discrete.
For gradual vesting, as an example, if an employee vests at 20% per year, if they leave after three years they will be 60% vested. With discrete vesting, say after five years, an employee is entitled to nothing until the five year post is reached, in which case they enjoy full benefits.