The Mushroom Kingdom Coalition HQ is the base for the MK Coalition, which includes Mario, Luigi, Wario, Sonic, Tails, Link, Arthur, Samus, Roll and Kirby, as well as all secret and clone characters. Except for Twisted Reality, the HQ can be accessed from the World Map at any time by hitting the pause button and selecting it. You can switch between characters here, learn about each character's different abilities and change game settings.
While the HQ originally appeared as an area that was entered on the world map, that option was deemed obsolete since beta 0.4 with the new pause menu and was removed.
Once again the HQ was updated in 0.5. Gone is the little goomba. Using < and > arrow keys, you toggle through the characters much quicker.