The Realm is a page that shows you how everyone in your Realm is doing. At the top of the Realm is your Realm's total networth, which is the sum of all the dominion's networth (which is the equivalent of your score). Networth is determined by your barren and built land, as well as military, spy and wizard strength. By selecting another Realm number, you can also view other Realms, and you will need to do so to find potential targets.
Here, premium account holders can also find the link to the Search page. The search page allows you to quickly filter a search for dominions by given criteria, including alignment, race, land size, networth, and guard status.