These words are related in meaning and can be confusing.
They all refer to being paid back money that is owed.
Rebate means "an amount of money that is paid back to you because you have paid too much or as an incentive for buying something." Here are a couple of examples:
We hope to get a big tax rebate this year.
My new car came with a $1000 rebate.
Note that rebate is sometimes used as a verb meaning "to make or give a rebate."
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Refund as a verb simply means "to give back money that someone paid for something" -- and usually it means that what was purchased was defective or unacceptable. As a noun it means "money that is paid back."
The bank will refund your late fee.
The rental car agency ran out of cars, so I got a refund.
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Reimburse is very similar in meaning to refund. It means "to pay back an amount equal to what has been spent." It is usually used when you pay for something for someone else, when you borrow from someone else, or when you pay for something now but you will be paid back later (such as when you have expenses for business travel).
I keep my gas receipts so that I can be reimbursed by my company.
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If you simply borrow money from a friend, you would say:
