Brain worlds are one of six biomes. Mine through dense brain matter, deadly metal spikes, pools of acid, and swarms of brains!
Undeveloped brain worlds have evokers that cause squads of brains to teleport near players at certain intervals. More specifically, each player will be attacked by 4 to 5 adult and/or large brains every 10 minutes, starting from whatever time they entered the world.
To destroy an evoker, you must place an inhibitor near the evoker, then hook the Inhibitor up to steam power by placing a collector over a steam vent, and then running brass pipes to connect the collector to the lower left block of your Inhibitor. A large explosion will occur, both the evoker and inhibitor will be destroyed, and you'll earn 500 XP (or more, depending on your rank in Order of the Moon).
Once all evokers are destroyed, brains can no longer drop in uninvited (although they'll still spawn as normal).
Brain worlds made their debut in May 2013, when three were created as part of the Brain Bazaar building competition. However it wasn't until December 2014 that they were fully released as generating (and purchasable) worlds.
The four chests of plenty at spawn teleporter in Brackhu Peak provide brain biome specific blocks, to get you started on building your own unique brain creations. You can find brain-related blocks in the Industrial section of your inventory.
Up until December 2014, you could only place brain-related blocks in one of the three brain competition clone worlds. It is now possible to place them in any biome.
It's rumored that someday inhibitors may have a chance to be recycled depending on certain skill levels.