The territory map allows you to see your neighbours and your own territory. Your territory is highlighted in red near the center of the map. You're surrounded by all lions that are of similar level to you, either 2 lower or 2 higher, or between. Your territory map may change frequently due to other users leveling or your leveling, as to put you in an area closer to your level range.
The territory map has been arranged by level rather than ID grouping so you can easily find people to attack or befriend. When you hover over the tiles, it shows a small window under your cursor. This information box says: who it is, how big their territory is, and their level.
You can participate in PVP in this area.
You can change your Territory's appearance in your den page at the bottom in "Edit your Details"