A pension is a defined benefit plan, rather than, e.g., a 401k which is a defined contribution plan. With something like a 401k, a set amount is put in, but there is no guarantee how much you will get out. With a pension, how much you get out (per month) in retirement is guaranteed.
In either case, vesting is the process of being with the employer long enough to have full rights to whatever retirement benefits you have earned. If you stay less than the vesting period, the employer will claw back the benefits you already earned and you could get as little as 0 (simply not vested), but some plans allow partial vesting, in which case the employer only claws back a part of what you earned if you leave early.
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