Huge Mushrooms are a block form of the regular Red Mushrooms and Brown Mushrooms. They occur naturaly on Mushroom Islands but can be grown by the player using Bonemeal. When Huge Mushroom blocks are destroyed they have a chance of dropping Red Mushrooms and Brown Mushrooms (Depending on which type it is).

To create a Huge Mushroom you need to place either a Red Mushroom or Brown Mushroom on Dirt/Grass/Mycelium. When placed on Dirt or Grass they can not be placed if the light level is too high(They can be placed on Mycelium even in direct sunlight). To get around the light level issue you just need to place a solid block 10 blocks above the block you want to place the mushroom on. With your Mushroom placed use Bonemeal on it. As long as it has enough room to grow (9x9x9 area guarentees it will grow) it will turn into a Huge Mushroom.