It works just like an additional credit card for say, a family member. It is NOT additional credit. It's just an additional way to access the same credit card and line of credit. You don't get a bill from Amex. However, if you use the card, you may well increase your credit utilization which is potentially negative. There are no fees (other than interest if you carry a balance). As long as your new "Amex" card is linked to the primary card, there is no annual fee. On the other hand, if you cancel your primary card, you will pay the annual fee.

My brother was sent one of these cards without asking for it. He didn't get any additional miles, however.