If you buy a basketball for your school team with your own money, and you ask your coach to reimburse you, you are asking him to pay you back. To reimburse is to compensate for an expense or loss.
The person who collects money at a college is the bursar, a purse is where you store money, and reimburse means to pay money back. All three of these words share the Latin root bursa 'moneybag.' If you want to be paid back for overpaid tuition, ask the bursar, Mr. Moneybags, to reimburse you from the schools purse.