Compound interest is the result of reinvesting interest earned rather than paying it out so that the interest earned in the next time period is added to the original principal and previously accumulated interest. In other words, you are earning interest not just on the original investment but on all of the accrued interest as well – earnings on earnings.
For example, if earnings were 10% per year and the initial principal investment was $1,000, the compounded amount after one year will be $1,100, after two years it will be $1,100 x 1.10 = $1,210, after three years it will be $1210, x 1.10 = $1331 and so forth.