Vesting is the schedule or process by which certain assets are eventually considered the property of an individual who uses them.
If your employer provides some sort of matching, flat, or profit-sharing contribution to your retirement account at work, you will probably not be allowed keep the entire amount that they contributed if you change jobs or retire before a certain number of years have passed.
This is because the employer contributions are usually vested over a period of time. The concept of vesting is present in several different contexts in the legal world, but it generally has to to with the gradual or eventual transfer of title or ownership of assets to an individual who has had use of them over time.
Vesting in retirement accounts means that your ownership of the amounts contributed by your employer starts at 0%, in which case you keep none of their contributions if you change jobs, and it eventually will become 100% yours if you stick around long enough.
The two main types of vesting are cliff vesting and graduated vesting. Cliff vesting means that you have no ownership until a certain time, at which point you suddenly have full ownership. Graduated vesting means that ownership is gradually transferred over a specific amount of time.
For example, if the matching contribution is $1,000 and the vesting period is four years, every year you stay with the employer, you will be able to take another $250 with you if you leave your job.