A Premium Bank Account is usually a fee-paying account where the customer pays the Bank a monthly fee and gets special features on the account.
In the example, of a Nat West Black account, Nat West state the following:
"With our Reward Black account, you can earn Rewards on selected household bills and your everyday spending. That’s 3% back on your council tax, gas, electricity, mobile, phone, TV and broadband. That means for every £100's of household bills you get £3 back. Monthly fees and terms apply."
These premium accounts are also known to offer extras such as Travel Insurance, Breakdown cover and even Mobile Phone Insurance.
Tip: Make sure you will definitely benefit from the upgraded account before upgrading to one. Your bank may contact you periodically to tell you about the possibilities and benefits of a bank account upgrade but make sure you either pop in to your branch or ask for the paperwork so that you can make an informed decision.