It's called a severance package. The company isn't giving you money to quit - you're working at-will and they can terminate your employment at any time for any reason. The amount is usually equivalent to a few months worth of paychecks.
What they pay you for is you signing away your ability to sue for wrongful termination. Because they can't really fire you for any reason.
It's also because companies want the managers and co-workers to know the company did right by the terminated employee. Laying someone off isn't fun. Seeing your co-workers get laid off isn't fun either. Severance keeps the process more humane.
Can someone tell me a little about this? Is this a situation where a company pays you to quit without firing you?