A pension is a regular payment, usually from a company you worked for, that allows you to survive without working after you retire.
In used to be common for someone to spend their entire career at one company, and then retire at 65 and receive a pension: regular payments of enough money to live on in old age. Nowadays, not that many jobs offer pensions, and it's hard for companies that do to pay for them, which is why you're likely to hear this word when people are arguing about budget cuts. It's also a verb: if you pension your employee, you give them a pension. How nice of you!