I stumbled on this contest and while am technically already disqualified from participating (the contest has bizarre rules), I did find the question intriguing enough to share my own perspectives.
This is one web definition of the word:
"Equanimity" comes from the combination of "aequus" and "animus" ("soul" or "mind") in the Latin phrase aequo animo, which means "with even mind."
It refers to the ability to maintain mental balance especially but not limited to challenging situations. With definitions out of the way, let me briefly state my take.
Life is essentially suffering. It challenges us in ways that may sometimes rattle our ability to cope. The first point of call for our defense mechanism in difficult life scenarios is our minds. How we react to the situations we find ourselves determines a great deal the kind of experience we get off it.
Equanimity is such an important ideology because it does not try to downplay the true nature of life with all its inherent suffering, malevolence, hatred, bitterness and all. Rather it conveys the message of accepting this nature of things and choosing not to react. The stoic philosophy probably conceptualizes this word best as it teaches us that no matter how much life throws at us, we would essentially be okay.
From a social point of view, I consider those who display high levels of equanimity with sound intellect and strong personal discipline. It is becoming increasingly difficult not to be reactionary in today's World as we're constantly bombarded on all fronts by our finances, socio-political environments, and our media. Refusing to be unfazed by all this allows us to pause, reflect and ponder on ways to reduce the amount of suffering that might be tossed our way.