This type of circuit is called an earth-return system any part of it connected to the car body is said to be earthed.
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.
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.
To guard against this, ancillary circuits have fuses. The most common type of fuse is a short length of thin wire enclosed in a heatproof casing often glass. The size of the fuse wire is the thinnest that can carry the normal current of the circuit without overheating, and it is rated in amps.