The Gathering Place is also known as Giant Tree, a place where PeakClan gathers to share the news of the Moon. The Leader jump onto the tree and the Deputy goes and sits on the roots while the Medicine Cat sits to the right of the tree.
The MoonFire is where the Medicine Cat meetings take place. There's a whole in the cave ceiling where when the moon is full it goes into the middle and makes the middle of the cave burst into flames. In order to dream the Medicine Cats simply lay around the fire and sleep.