In Europa Universalis II, a coat of arms is a small, shield-shaped icon used to represent various countries. Each coat of arms is unique. For example, Eire's green with gold harp, France's blue with gold fleurs-de-lis, the Ottoman Empire's red with white crescent and star, Sweden's blue with three gold crowns. In most cases, but not all, the design is similar to that found on the country's flag as well.
Your own country's coat of arms is displayed in the center button along the top of the controls window. Clicking that button will display the country screen with your country selected, from which you can access the domestic policy screen and the religion screen.
On the Country Selection screen, a number of coats of arms are displayed in a row along the upper edge. These countries will be the ones shown in the ledger graphs in your game, and can be altered by right-clicking on them and replacing them from a pull-down menu. Left-clicking on one of these will designate that you wish to play that country in the scenario you are loading. Using a combination of right and left clicks, you can thus access all playable countries in any scenario.