A reimbursement is a repayment for money you've already spent. When you travel for work, you get a reimbursement for your work-related expenses, like hotel bills and plane tickets, but you'll have to pay for that trip to the circus yourself.
Reimbursement comes from the Latin root words re, meaning again; in, meaning into; and bursa, meaning purse. So the word reimbursement literally means in a purse again. After your parents' basement flooded, they paid to repair the damage and then got a reimbursement from the insurance company, so that they could put the money they spent in their purse again.