Compound interest is interest computed on a loan or deposit based on the original principal and the cumulative interest from previous periods. It's essentially "interest on money that was previously earned as interest." When opposed to simple interest, which is determined just on the principal amount, this permits your balance and interest to grow at a quicker rate.
The rate at which compound interest accumulates interest is proportional to the number of compounding periods; the larger the number of compounding periods, the higher the compound interest rate.