Compound interest is where you earn interest on the interest you've already earned - whilst it sounds complicated, it can have benefits for savings and investments accounts.
For example, if you deposit an amount into a savings account with compound interest, you will earn interest on that deposit amount in the first year.
In the second year you would earn interest on the original amount, presuming you don't add or take out any money. But you would also earn interest on the interest you earned in the first year. For every year after, you will continue to earn interest on the original amount plus all the interest from following years.
With a compound interest savings or investment account, you may be able to grow your funds quicker than if you have an account with simple interest.