The World Map is composed of various regions that you must traverse on your quest to save the Princess. Each region is composed of 10 battles, including one Boss Battle. Defeating the boss for a region will unlock the next one.
Pictures at each level will show you which of your friends currently have the top score for that battle. Highlighting the level with your cursor will show you the level of the enemies there, how many there are, how much gold you will earn, and any items or equipment that may drop from winning the battle.