Maps will usually only show you the surface of the current world you're in, however while the map is loading you might sometimes be able to spot the overview of deeper levels like for the Corruption layer (where red clouds indicate corrupted leaves) or other underground layers for a short period of time.
You can open the map ingame by pressing "M" as the default key (customizable). You can then change from the overview map showing the whole world to a closer look at a part of the area you're currently in by clicking on the orange magnifying-glass icon in the lower left corner next to the map.Each world is divided into 26x26 (676) areas, and each area is divided into 8x8 = 64 possible claims (43,264 all in all). Undiscovered areas are hidden by a "fog of war" (as it's commonly called in videogames), until you will uncover them by simply entering these areas. Your area map will only show you 5x5 claimable regions, however the whole area is 8x8 optional claims.
Currently (as of April 2016) there are 8 reference worlds available for Creativerse, as revealed here: http://steamcommunity.com/sharedfiles/filedetails/?id=634088783 , where you can see all of their whole surface maps unveiled.
The large overview map will show you players (use mouse-over to see their names) and claimed land - in different colors depending on your personal authorizations there.
Red Claims provide you with mere visitor-rights, so you cannot mine or harvest anything there (except for randomly spawning Treasure Chests and loot bags of creatures that you kill/dismiss there). Yellow claims grant you more rights like building, and blue claims are those that you have claimed yourself, so you're the owner with full authority there.
In the area-view of the map you can see claims as well as players, plus you can even spot creatures moving there if you look closer, also Teleporters and treasure chests, although sometimes these might be a bit hard to make out. At night all areas are shown just as dark on the map as the 3D surrounding is, and regions lit by lighting become very well visible on the map. As soon as you change the world by building something that is visibly from above, this will also become visible on the area map.
You can click on the small arrows on the compass in the lower left corner to move to other areas than your current position, however even unveiled areas will be shown blurred out, as mobs and treasure chests will usually only start spawning there when players come close.