It's a fee that your city/town tacks onto your bill. Basically, the cable company gets charged a fee by the city to run cables and such across public property and you as a pay tv costumer foots the bill.
Basically the cable company is paying rent to the city/town to run cables on the poles. (A franchise fee is not a tax.) It is levied on basic service and is typically 5% of the revenue from basic service. If you only have internet and/or phone from the cable co and do not have TV service you will not pay a franchise fee.