Atlas of the World utilizes a number of good ideas, but doesn't fulfill its promise due to a lack of additional data, features, or tools that would make this a fun app to use. In effect, all you can do is view the population data for each country labeled on the map, or states in the United States. This limited interface makes clever use of the map data drawn from Google; but beyond the overlays, there is little else here to keep you occupied.
When you open Atlas of the World, you can select World, North America, or Landmarks. World Atlas allows you to tap any one country and see its population. The North America atlas is the same for the United States, actually excluding other North American Countries: Mexico, Canada, and the Caribbean. At the same time, Landmarks is a cool feature, showing you an overhead view of 200 different landmarks around the globe from satellite distance, but with no data on those landmarks to flesh it out. In effect, Atlas of the World has a single trick up its sleeve and once that is worn out, there are no additional features to keep you occupied. This is less an atlas and more an annotated map.
If you are interested in learning more about world populations and country names or if you want to see satellite views of various world landmarks, which is admittedly very cool, then Atlas of the World is a fun distraction for a few minutes. Beyond that, however, it lacks the depth needed to be a true atlas for your iOS device.