The lawful right of an individual or entity to gain access to tangible or intangible property now or in the future. A vested interest is an entitled benefit, which can be conveyed to a separate party. There is usually a vesting period before the claimant can gain access to the asset or property. Due to the right of ownership, the benefit cannot be taken away i.e. the vested funds are not contingent on any action or inaction.
Explained further: This can most notably be seen in employee pension plans. Contributions are made under the stipulation that retirement funds will be entitled to the participant, known as a vested right. The vesting period (period of time before access is granted) varies among pension plans. The withdrawal amounts can be restricted to a certain percent each year. For example, after waiting the five year vesting period, Peter was only allowed to withdraw 20% of his retirement fund each year.
Definition courtesy of Investopedia