Just the mention of the term equanimity brings up a notion of what is correct and noble. The word comes from the Latin aequanimitas, composed from aequus, meaning "even or equal," and animus, which means "mind or spirit."
From the Dharma point of view it means that no matter what the circumstances are, particularly with respect to your own behavior, there should be neither an emotional response that reinforces clinging and craving as a result of external consequences nor an aversive response that reinforces that form of behavior as a consequence of an external response that is not agreeable.
Put then into ordinary terms... If you are praised then ignore it. If you are condemned then ignore. In all cases maintain a state of being unaffected by consequences.
That appears very correct and agreeable, but that state should not be confused with the INTELLECTUAL INDIFFERENCE which is its Identity counterpart.The Buddha described a mind filled with equanimity as “abundant, exalted, immeasurable, without hostility and without ill-will.”
The Abbhidhamma sets out two concepts regarding Equanimity. There is Upekkha and Tatramajjhattata.
The former, Upekkha, has the association of Equanimity arising from understanding. It encompasses the idea that if one understands there is nothing to forgive with regards to the consequences and equally nothing that is worthy of clinging to such as praise and blame, success and failure, pleasure and pain, fame and disrepute.
The second, tatramajjhattata, is a compound made up of “all these things,” “middle,” and “position.”
The idea than is to take up a position that is “to stand in the middle of extremes.”
This requires a certain stability, calmness, an internal integrity that demands the natural virtue and confidence which arises from the development of correct attitudes and intentions maintained with effort and diligence.
You will be able with discipline to maintain an equanimity, but for it to be completely internalized at a level where it will be automatic, rising with all intentions, a correct meditation is required that manages to pass beyond access to the fourth level of Buddha's Jhana Meditations.