A Carnet card is basically a credit card for fuel. Some airport fuel bowsers (to fill up your GA aircraft) accept them as a swipe. They also sometimes prove useful at an offline port where you don't have a pre-existing fuel contract.
Edited to add - I used to wonder why we carried them on a heavy jet aircraft, until one day we diverted and ordered our fuel. The nice refueler asked "and how would you like to pay for that". I wonder if the captain's credit card would have had a limit high enough to pay for 64,000 litres of Jet A1 had we not had a carnet card
