The two components are connected in series so that the varying resistance in the sender will affect the position of the needle on the gauge.
If the cable overheated, there could be a fire. The fuse prevents that happening, because its thin wire will melt and break the circuit long before the cable itself can heat up and burn. Some cars have only two fuses. One rated at about 30-50 amps protects components wired through the ignition switch — flashers, wipers, heater-motor and instruments.
Depending on the fuse design, it is sometimes possible to tell whether it has blown by holding it up against a light; a break in the wire inside may be visible. Another clue is blackening of the glass cover. If there is no visible sign, check by fitting another fuse of the same rating; if that cures the trouble, then the fuse was to blame.
The sudden surge of high current in a short circuit makes the fuse wire melt, or blow, breaking the circuit. When this happens, see if there is a short circuit or a disconnection, then install a new fuse of the correct amperage rating (See Checking and replacing fuses).