Can you tell me how true is the phrase the brain is a muscle?

Just not true: That's like saying I'm a dandelion. Both brain and muscle have excitable membranes and cells that respond to each other. Brain lacks muscle's defining contractile filaments. Muscle lacks brain's defining synapses between nerve elements. You can't change your brain's shape by exercising, but gains in learning knowledge and skills help you in many ways while training muscle helps general health.