A Packaged Bank Account, also known as an upgraded account, fee-paying account or bundled account, is a bank account where a monthly fee is paid in return for some add-ons which the bank identifies as being of benefit to you.
As an example, many banks offer Packaged Bank Accounts with extras such as Travel Insurance, Mobile Phone Insurance, Breakdown Cover, special rates or interest free overdrafts.
They might be called things like “reward”, “premium”, "premier" or “gold” accounts to elevate them from normal current accounts.
For example, here is a screenshot of Nat West Bank's current list of bank accounts. You can clearly see that some of the accounts come with different amounts of rewards/benefits and the monthly fee will increase accordingly.