Here's the key difference. Simple interest refers to interest that is just paid on the principal. On the other hand, compound interest refers to interest paid on the principal as well as on any interest that has already accumulated.
Consider this simplified example. Let's say that you have two investments. One is a bond that cost $5,000 and pays 6% simple interest. The other is a 24-month certificate of deposit (CD) that pays compound interest at the same annualized rate of 6%.
After two years, the simple interest bond investment would be worth $5,600. You’d receive 6% of the principal ($300) every year.
On the other hand, the CD would pay 6% the first year, giving you $5,300. However, the second year's 6% yield would be based on $5,300 -- not on the initial principal balance of $5,000. So, 6% of $5,300 is $318, bringing the balance at the end of two years to $5,618.
Generally speaking, compound interest will result in a higher amount of money over time, all other factors being equal. And over long periods of time, it can make a big difference.