APY is the Annual Percentage Yield, and is similar to APR. Except APY refers to interest you get instead of interest you pay. It is a way for the investor to determine the actual rate of return and compare different investment products.
Here is an example:
One bank is offering certificates of deposit paying 6%. Another bank is only offering 5.9%. Which is the better deal? It depends on the APR which they must reveal to you.
It seems the first bank is not compounding the interest. It is only paying simple interest of 6%, so at the end of the year you have $106. The second bank is compounding your interest monthly, so at the end of the year you have $106.06. The first bank had an APY of 6%, but the second bank had an APY of 6.06%. Not a vast difference, but you see the concept. Over a period of many years, these small differences can add up, and that is why knowing your APY is important.