Could you please explain the meaning of equanimity?

Answer of Lama Ole Nydahl:

Equanimity means being constantly aware that we are all already buddhas, whether we know it or not. It means having no attachment and aversion, not dividing anything into categories like “good” or “bad,” and always wishing everybody all the best. Of course one still has to act and know what is right or wrong for oneself, but all this should happen without anger or bad feelings towards others.

The best antidote to jealousy and all kinds of expectations is very simple: you make yourself infinitely rich in your mind, and that way you can give others all the happiness in the world. Every time you think of someone you want something from—for example, you want him to love you—think, “May he have all the happiness imaginable.” Because if you feel rich yourself and are in the position to give and to wish the other something good, then you will never go wrong.

A situation gets difficult if it feels small and narrow. If, for example, your former partner is now with someone else and you think, “Oh, right now he is with her doing this or that thing which is so wonderful and special and which we always did together…”—this is a thought that catches you, that you won’t get rid of. This is a narrow situation. But if you wish him fifty dancing girls or—for the ladies—as many mustachioed officers on horseback as she wants, if you wish everything in abundance for the other, then it is not personal anymore but rather like watching a Disney movie. And suddenly the problem dissolves. With this approach, a small, personal thing turns into something profound, and you can grow very quickly by using this way of thinking as a turbocharger.

All at once, you get out of the darkness and really start to shine. You can crack jokes about things that were very touchy to you before, and work with the situation without limitations. This gives a lot of strength and has an exceedingly liberating effect. Then, in addition, you might be lucky enough to get an extra bit of good energy from the teacher, who pushes you in the right direction to quickly discover your own power. Wishing everyone all the best is really very good.