According to Merriam-Webster dictionary, "vested" means to be "fully guaranteed a legal right, benefit or privilege." Vesting occurs either gradually or all at once upon the finalization of ownership of an entity.
The term "fully vested" usually applies to individuals who receive retirement, profit sharing or stock option benefits from the company that employs them. For example, when an individual goes to work for a company, he might receive part of his vested interests in his employee profit sharing, stock option and retirement plan every four to five years that he works for the company. Therefore, when he retires from the company after 20 to 25 years, he leaves the company fully vested with the entire range of benefits at his disposal because of his completed service to the organization.