I Need to Understand Some Installation Terms

Installation of what? and where?

Main Cables:- Large wires carrying electricity from one place to another.

Sub Main Cables:- branch conductors/wires connected to a main.

In residential wiring, you may have 1/0 AWG (67.43mm^{2 )} feeding the service panel and #12 AWG (3.3mm²⁾ branching off in a daisy chain feeding the sub-circuits.

Isn't the latter technically a 'branch circuit'? I would think a 'sub-main' cable terminates in distribution panels at both ends.

Not in the UK. 3.3mm² cannot be had here, as it is a non-standard size in any conductor material, and there are no pre-calculated solutions for this particular conductor size whereas there are for other sizes. 1, 1.5, 2.5, 4, 6 and 10mm² are typical sizes in copper. Usually, 2*4mm² is the most that can be fitted into the receptacle on the rear of the outlet/switch/socket/whatever whereas the larger sizes will be attached to heavy load appliances such as cookers and power-showers using a non-insertion method of fastening.

The "tails" coming from the meter to the dis' board would usually be 16 or 25mm² copper, usually double-insulated singles.

However, there are other solutions that will respond affirmative to calculations as regards suitability.

Off-topic, but I sometimes have a problem trying to rationalise some members names.

Yes. A qualified Electrician can do this.

One won't find qualified Electricians by the name of Google. One will by using the local telephone directory.

Read up on your local electrical codes and standards, the answer is there.

If you are having trouble understanding the Google results you should either take some courses to get a license or hire a professional.