Interest is simply the amount charged to someone for borrowing money. So to a borrower the interest is the cost of borrowing the money, and to the lender the interest is income gained from lending the money out. Interest is expressed as a percentage rate.
There are two main types of interest; simple and compound. Simple interest is charged on the initial principal lent out to the borrower. Compound interest is interest on both the principal and the compounding interest that is paid every period.