Some comments on "evenness of mind ... under stress" in Fully Present, a book about mindfulness and meditation by Susan Smalley and Diana Winston:
When your mind is relaxed and at ease and you feel impartial and balanced, then you are experiencing equanimity. We have all had the experience of being in the midst of a difficult situation that would ordinarily cause us a lot of pain and yet, in spite of the conditions, deep down we somehow feel okay about the situation. This is a feeling of equanimity. Many people report, for example, that they have occasionally received bad news with surprising calm and centeredness. With equanimity, rather than being tossed and turned by the ups and downs of life, your mind feels balanced and even and you are not overreactive—neither suffering nor bliss overwhelms you. Equanimity is a very pleasant state of mind characterized by a sense of "okayness" and well-being.
Equanimity is not a state of disassociation or dispassion but in fact a very connected state of mind. It is a misconception that equanimity places you above worldly concerns or makes you apathetic; neither is the case. With equanimity, you are very engaged in life and not the least bit apathetic. You care passionately about a situation, yet your happiness and well-being are not tied to the outcome of the situation. Somewhere deep inside you recognize that you have preferences, but that your happiness does not depend on fulfilling them. So you stand up for yourself and what you believe in, but you are willing to let go of the results of your actions.