The Clockwerk brain is the part that possesses Clockwerk's mind and being. Without this part, Clockwerk would not reactivate himself.
Sly 2: Band of Thieves
The brain is mentioned a couple of times in Sly 2: Band of Thieves. The first being in He Who Tames the Iron Horse. In Cabin Crimes, one of the cabins Sly enters has Jean Bison, and he is having a conversation with Arpeggio. A short way into the conversation, Jean Bison mentions buying the brain off of Arpeggio, but Arpeggio mentions that Jean Bison already has the lion's share of the parts, being the Clockwerk Lungs and the Stomach.
The second time is in Menace from the North, Eh? When Sly exits the Safe House, Bentley talks to him through his Binocucom. Bentley says that if they are ever going to take a peek at the brain, they'll need to sneak aboard Arpeggio's Blimp.
Trivia
- The Clockwerk Brain is briefly seen in Sly Cooper and the Thievius Raccoonus as you destroy Clockwerk.