The map is an addition to the HUD of a player, it allows the player to see nearby biomes, dungeons, lairs and other players. Biomes would be represented be colours and logos like green colour and sunflowers for the Peaceful Hills, orange colour and cactus for the Desert Frontier. Dungeons are represented by a castle-like logo, and covered by a Red "X" when already completed.
The map is accessed by pressing M on your keyboard. You may also press M again to stop looking at the Map. The map will also disappear if you move and can be accessed again by pressing M.