A territory is a specific place you can capture/own in Risk. In the original Risk, these are countries (or parts of them) of the world. Other examples include Planets, in Star Wars Risk.
Capturing Regions is the primary objective of Risk. The more territories a player has, the more troops the player is entitled to. Territories are split into regions, when a player owns all the territories in a region, they are entitled to a region bonus (extra troops).