Banks usually pay a low interest rate on their customers' deposits and then loan that money out or invest that money directly in the economy. The bank gains a higher rate of return on its investments and is happy to pay you a lower interest rate for the use of your money.
As a general rule, what you really have there is a "loaning" account, rather than a "savings" account. You are lending money to the bank, and they are making a profit off your money. You have no choice but to reverse the situation if you want to make your money work for you. You must become an "owner," not a "loaner." You must learn to "bypass the middleman."