Compound interest is interest calculated on the initial amount invested and any interest that has been paid since.
This works by taking the interest you are earning each week and adding it to your original investment, so that your total investment that is earning interest grows - allowing you to benefit from larger interest payments.
As an example:
If you were to earn 10% interest per annum on 1 BTC with no compounding, you would earn 0.10 BTC interest in one year.
If you were to earn 10% interest per annum on 1 BTC with weekly compounding, you would earn 0.10506479 BTC.