A balance transfer fee is a one-time fee you are charged when you transfer a balance from one credit card to another. The fee covers the administration of the actual transfer of funds. Most balance transfer fees are somewhere around 3-5%, but many issuers offer lower fees or even waive them entirely for a promotional period. Check the fine print for time restrictions if a card is offering a transfer fee promotion; sometimes the transfer must be initiated on your card application or within a certain time frame of your being approved for the card (i.e. 30 days). Some cards also charge a minimum and maximum balance transfer fee, so take this into consideration when deciding how much to transfer. 

A balance transfer rate, on the other hand, is the interest rate you are charged each month on the current balance of funds transferred. Credit card issuers also offer promotional balance transfer rates quite often. For example, a credit card with a "0% intro APR on balance transfers for 12 months" means that you'll be charged no interest on any balances you transfer for a full year. If you have not paid off the transferred amount by the end of the promotional period, you will incur interest charges on the remaining balance.