How do you raise your territory rating?

You gain territory points by repelling invasions from other teams.

Non-Conquest Invasion missions will degrade the "AP" (displayed as the meter on the right of your territory list, if you own them) of enemy territories (randomly selected) which, if at zero, will cause the territory to revert back to AI control if the owner does not increase the AP (by defending) within a specified period (it is set to 12h on Japanese servers, not sure on US).

Stronghold missions will raise your Territory Rating (both conquest and regular ones). Territory Rating will also go up if the defenses you set up destroy enemies that invade the territory, though its basically random as to when someone attacks if your not sitting there in a Stronghold Mission prep screen.

Regular Invasions will give you Team Pts and damage other teams territories so that they will defend them, although which territory gets damaged is random as well.