If your dog barks whenever someone walks through your yard, it might be because she's territorial, or inclined to protect her territory from trespassers.
A person — or an animal — who guards or defends the area she considers to belong to her is territorial. You can also use the adjective to describe anything relating to the territory itself. For example, territorial boundaries are invisible lines that mark the division between one country, or territory, and another. The Latin root, territorium, "land around a town," comes from terra, "earth or land."