The Monkey Brain is a concept described in Jay Shetty’s book Think Like A Monk - Train Your Mind for Peace and Purpose Every Day.
In the Hitopadesha, the mind is described as a drunken monkey that’s been bitten by a scorpion and haunted by a ghost. If each branch on a tree is a thought, the monkey randomly swings between the thoughts. The Dhammapada has a verse in it that reminds us that the mind needs to be shaped and trained, just like archers crafting their arrows or irrigators leading water where they want it to end up.
Jay describes the mind in two parts. The Monkey Brain is like a child, crying when it doesn’t get what it wants. The Monk Brain is like an adult, is able to think long-term and rationally. The Monkey Brain can’t be and shouldn’t be fully suppressed, as the Monk Brain can be too controlling, leading the Monkey Brain to be bitter and resentful.