With simple interest, interest is calculated based on the original deposit only. The amount of interest earned in 1 year does not affect the amount of interest earned in following years.
With compound interest, interest is "compounded" or added a specific number of times per year. After the interest is added, the next time it is calculated, the amount is based on the total amount in the account.
For example, if we deposit $100 at 2% compound interest that is compounded yearly, the first year our interest would be 0.02(100) = $2. Before the interest is calculated the next year, this $2 is added to the account, making it $102. This is the value we use to calculate the next year's interest: 0.02(102) = $2.04.
Because of this, compound interest grows more quickly.