The annual equivalent rate tells you what a savings account pays over a whole year once the interest credited during the year has started earning interest of its own. British banks quote it as the AER; American banks call the same measure the annual percentage yield, or APY. Both exist so that an account paying interest every month and one paying once a year can be compared on equal terms.
The working is compound interest over a single year. Take the advertised nominal rate, divide it by the number of times interest is paid, add one, raise the result to that number and subtract one. A 4% rate paid monthly gives (1 + 0.04 ÷ 12)^12 − 1 = 4.074%; the same 4% paid once a year stays at 4%. In the US, Regulation DD fixes the method: APY = 100 × ((1 + interest ÷ principal)^(365 ÷ days in term) − 1), on a 365-day year, so a bank cannot flatter its figure by choosing a convenient day count.
The AER is the savings version of the effective annual rate, the general measure that applies to borrowing too. It is not the APR on a loan, which also counts fees and, in the US, leaves out compounding altogether. On a variable account the figure assumes today's rate holds for twelve months, so it describes the rate now rather than promising what the year will pay.
For comparing accounts the AER or APY is the right number and the frequency of payment is already inside it. That frequency matters less than people expect: at 4%, moving from yearly to monthly payments adds less than a tenth of a percentage point, while a better headline rate can add far more. The compound interest calculator shows the figure beside its result, worked out from the rate and compounding setting you choose, so you can check it against the one a bank advertises.