Electricity is supplied to your home via a service cable which is terminated into a chamber that contains a fuse.
This fuse protects the complete installation and is the responsibility of the electricity supplier. The meter is fed from this fuse, this can be integral as shown below or with visible cables.
In older properties these cables would be red and black, in newer properties these cables have an additional grey sheath to protect them.
Everything after the meter is the responsibility of the consumer, including the cables from the meter to the consumer unit.
The consumer unit is the main part of the consumers electrical system, from here all the individual circuits are fed and protected by a fuse or MCB (miniature circuit breaker). The consumer unit also incorporates a main switch where the entire electrical supply can be isolated.