Why do we need earth wire and fuse?

Simply put, electric appliance can be very simple with just a live wire bring in the current and a neutral wire to bring the current out. The appliance can just work like this forever (without the hassle of having earth wire, fuse etc), provided there is no electric fault developed.

Both the earth wire and the fuse are safety features to protect the user and the appliance respectively. Take a look at the video below to understand the rationale.