The annual equivalent rate (AER) shows you how much interest you would earn on a savings account, taking into account compounded interest and any introductory bonus interest rate you get. It is designed to make it easier to compare the interest you will receive over a year between different savings accounts.
For example, if you are paid interest monthly on an account, the AER takes into account the interest you will earn on the initial deposit plus the interest you will earn on that monthly interest. In that way it differs from gross interest, which does not include any interest you earn on interest. If you are paid interest annually, then the gross rate and the AER may be the same.
An AER does not take into account any tax you may have to pay on your savings interest.