The black cable wire is connected to the top terminal on the switch and spliced to the black and blue wires at the fan at the other end. The neutral source and ground are spliced through to the white and ground connections at the fan.
The hot wire to the fan in a fan/light kit will usually be black and the light wire will be blue. The white wire is usually the neutral which is always connected directly to the source neutral, either at the source or through a splice in the switch box. The white wire may also be used to carry current when necessary.
This page contains wiring diagrams for ground fault circuit interrupter (gfci) receptacles. Included are diagrams for multiple gfci’s, a protected standard duplex receptacle, and a protected light fixture. Wiring for a switch and gfci receptacle in the same box is also shown to protect the switch and light or to protect other receptacles in the circuit. To wire a gfci circuit breaker see this link and wire a gfci switch combo at this link.
Use this wiring when the source is at the fixture and you want to control the feed to both components with the same switch. Three-wire cable runs from the fan to the switch box and the source neutral is spliced to the white wire and to the fan neutral.