With equanimity, your initial reactions to things-- reach for the carrot, push away the stick-- are left in a mental mud-room so that the interior of your mind remains clear and clean and peaceful.
With equanimity, what passes through your mind is held with spaciousness so that you stay even-keeled and aren't thrown off balance. The ancient circuitry of the brain is continuously driving you to react one way or another-- and equanimity is your circuit breaker.
Equanimity is neither apathy nor indifference: you are warmly engaged with the world but not troubled by it.
The primary point of equanimity is not to reduce or channel that activation, but simply not to respond to it. This is very unusual behavior for the brain, which is designed by evolution to respond to limbic signals.
Since your brain doesn't naturally stay engaged with neutral stimuli, you must make a conscious effort to sustain attention to them. Through sensitizing yourself to the neutral aspects of experience, your mind will become more comfortable staying with them, and less inclined to seek rewards or scan for threats.
Buddhism has a metaphor for the different conditions in life. They're called the Eight Worldly Winds: pleasure and pain, praise and blame, gain and loss, fame and ill repute. As you develop greater equanimity, these winds have less effect on your mind. Your happiness becomes increasingly unconditional, not based on catching a good breeze instead of a bad one.
-- All notes taken from Buddha's Brain, pp. 109-117
