From the Introduction:
Across the seas or perhaps trackless deserts, places of legend in stories told by sailors who have seen the edges of the world, these Arcane Kingdoms are beyond the knowledge of many. But here, collected in these pages, is all the information known of these realms.
When adventurers find these lands, they may add new understandings, upset accept wisdom, and possibly even forge a new history for these dominions.
What Do I Do With This?
Whatever you want.
The purpose of Arcane Kingdoms is to provide a small amount of information on a collection of nations that could be used in your game. How these are used depend on what you need. If you are running a "points of light" campaign, your players' characters may find themselves near the edge of the map, and begin asking what's beyond that. You may need a background for a mysterious character, some place beyond the confines already known in your campaign. One of your players may want a character who likewise comes from beyond the known lands.
Basically, this saves you from thinking up some foreign lands, for whatever purpose they might be needed.