An AOC is an Aircraft Operators Certificate which is basically the piece of paper issued by the CAA that allows a company to operate aircraft for the purposes of public transport and other commercical work. It is certainly not free (talking 10 to 20k), requires a large amount of paper work including an operations manual, affects the way the aircraft is maintained and who flys it.
I must admit that I was sorry to see that an AOC is required - it would be nice to have your own call sign.