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).
A headlamp bulb, for example, is designed to have a degree of resistance so that it consumes a certain current to glow normally. But there are at least two headlamps in the circuit. If they were connected in series, electric current would have to go through one headlamp to get to the other.
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.
Often, however, it is hidden away, perhaps under the dashboard or down in the front knee-well. The car handbook usually gives the location, but without a book finding the box can prove difficult. Get to know where it is before anything goes wrong.