Balance Protection
  
"For an additional fee" is the beginning phrase to almost every bad deal available to every consumer...ever. It basically just means "this is going to cost you way more than it's worth, but please do it."
Balance protection is just such a deal. If the card owner buys the balance protection plan and is subsequently injured or unemployed, the balance protection plan will pay the minimum monthly payments on her card balance (that's good for the credit card company, not so good for the card holder) to keep the card from going into arrears. Sounds good, but there are better ways of accomplishing the same thing (disability insurance, cash reserve, not carrying credit card balances, etc.).
Typically, the additional fee for the balance protection is a specified percentage of the existing balance on the card, and is added to the monthly statement. It's basically the bank selling you a very high margin (to them) insurance product. Instead of buying it, like...why not just pay off your bills on time?