In general being “vested” in something means that you have a legal right to retain it.
As an example, you might have a pension that vests after ten years — if they fire you after nine and a half years you have zero pension, but if they fire you after ten years and one day you have a pension based on ten years of service.
As a more modern example, you might have an employee stock grant or options that starts to vest after one year of service, with subsequent vesting events every six months — on those calendar dates you come into ownership of chunks of your promised stock or options.
Pensions aren’t common any more because they are a liability for the company — a monthly payment to former employees for as long as they live, often with health care benefits that keep getting more and more expensive. A 401K, on the other hand, is a simple deposit into a retirement savings account, with no future obligations.
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