What compounding actually is
Interest that is paid out stops working. Interest that is added to the balance starts earning interest of its own. That is the entire idea, and everything else on this page is a consequence of it.
The consequence worth seeing is that the effect is not linear in time. Over one year, compounding is worth almost nothing: there has been no interest to compound yet. Over ten years it is noticeable. Over thirty it is most of the answer. Set the term to one year on this page, then to thirty, and watch which part of the split bar grows.
The compounding cycle, and why the table is here
A nominal rate of five per cent means different things depending on how often the interest is added. Added once a year, five per cent is five per cent. Added monthly, each month's interest starts earning in the next month, and the year ends slightly higher. The comparison table on this page runs your money through all four cycles at the same rate so the difference is a number rather than a claim.
Two things about that difference are worth knowing before you go shopping for it. It is small compared with the rate itself: moving from yearly to monthly compounding at a normal savings rate is worth far less than a quarter point on the rate. And it is already included in the figure most banks are required to advertise, which is why that figure exists.
Nominal rate, APY and AER
The rate typed into this page is the nominal annual rate, and the compounding cycle is a separate field. Advertised rates usually work the other way round: they fold the compounding into a single number so that two accounts can be compared without asking how often each one credits interest.
In the United States that number is the annual percentage yield, defined under Regulation DD. In the United Kingdom it is the equivalent annual rate, which the FCA's rules require alongside retail deposit advertising. Both are higher than the nominal rate whenever interest is credited more than once a year, and both are the right number to compare two accounts with.
If a bank quotes you an APY or an AER and you want the balance this page would show, enter the nominal rate they also disclose and pick their compounding cycle. Entering an APY as if it were a nominal rate and then compounding it monthly counts the compounding twice.