Thin wires conduct less easily than thick ones, because there is less room for the electrons to travel through. The energy needed to push current through a resistance is transformed into heat. This can be useful, for example in the very thin filament of a light bulb, which glows white hot.
There are many fuses, each protecting a small group of components, so that one blown fuse does not shut down the whole system. Many of the fuses are grouped together in a fuse box, but there may also be line fuses in the wiring.
The individual fuses in the box are usually numbered, so that sorting out which one may have blown is simplified by referring to the numbered list in the handbook. This should tell you which fuse protects which circuit. Where they are not numbered, take out each fuse in turn and see which component stops working.
However, it is always advisable to check the circuit also, in case a fault in it caused the fuse to blow. For example, failure of an electrical component or damaged insulation on a cable can cause a short circuit, resulting in a sudden massive increase in current.