A pension is a benefit paid to people retired after their employment by their employer or a third party on behalf of the employer.
Pensions can be defined as either "defined benefit" or "defined contribution".
In a defined benefit plan, the amount paid to the retiree after employment is known (or is easily calculated); what is unknown is the amount required to provide the benefit as it depends on interest rates (often over a long period of time). Also they are not portable (in most cases); if an employee leaves the employer outside of retirement, the pension is greatly reduced if not completely eliminated altogether. While defined benefit pensions are still common in the public sector (the Federal Employees Retirement System, and its predecessor the Civil Service Retirement System, are among the largest and best known), they are rapidly disappearing in the private sector.
In a defined contribution plan, the amount contributed to the plan is known (or is easily calculated, and may include amounts matched by the employer); what is unknown is the amount the retiree will have upon retirement as it depends on performance of the underlying investment (and it is possible that the amount could be zero, if the investment is in company stock and the company later ceases to exist). They are also usually portable to an extent: usually individual contributions and associated earnings can be taken to another plan (but company matching amounts and associated earnings may only be portable if an employee is "vested" in them, usually requiring a certain amount of time employed). Individual retirement accounts and 401(k) plans are popular types of these plans; in the Federal civil service the Thrift Savings Plan is the defined contribution portion of the overall retirement system.
Social Security payments can supplement the pensions of individuals, in addition to other savings that a person may have to fund retirement living. However, it will only repay a portion of income (and the higher one's income the lower the percentage).