What is the small map in the bottom right corner?

The small map in the bottom right corner indicates the map style that you have selected. The background map shown in the map design area is meant as a reference map to define your map size and dimensions. You can see how your map will look like with the applied mapstyle before downloading it by clicking 'Save' and Generate Map in the 'Generate Map' panel. Then you can click on the magnifying glass on the map thumbnail when it has been rendered and see the map as it will look when you download or embed it.