The Forest Hideout is a building that is the base of Boshi and his group, the Yoshi Baddies. It first appears in Super Mario: An Evil Rising.
Super Mario: An Evil Rising
When Waluigi comes to Yoshi's Island, he is given a mission by the Yoshi Ruler to stop Boshi and his group. Waluigi goes through nearly the whole group, defeats Boshi and then heads back to the Yoshi Ruler. Later, when the Mushroom Behemoth is going on a rampage, Boshi somehow modified the hideout to fly and you can see it flying away from the crushed Yoshi's Island.