The word commission has several very different meanings, but in its most basic meaning, commission is the act of passing a responsibility to someone else. If you receive a government commission, that means you have been assigned a task by the government.
Another common meaning of commission is the amount of money an employee earns when they sell something: In addition to his salary, he gets a 1% commission on each sale. A commission is also an order for someone to do something and get paid: The artist received a commission for a new painting to hang in the building lobby. And a commission is a high-ranking position in the armed forces, or a special committee that controls or investigates something.