Equanimity as a virtue is a life free from pain, suffering and inner suffocation.
It means freedom from attachment and abhorrence towards anyone or anything i.e. one neither has attachment towards those who offer him flowers nor any hatred towards those who may choose to insult him. Such is the virtue of equanimity. One remains neutral and balanced in every situation, be it good or bad.

“Equanimity is when abhorrence does not arise during the circumstances of abhorrence and attachment does not arise during the circumstances of attachment.” - Param Pujya Dada Bhagwan.

By maintaining equanimity, we experience inner peace and stability in every circumstance – good or bad. There is no preference there for any particular situation, thing or person, there is nothing like ‘I love this or I do not like that or I am unable to gel with this person well.’
What does attachment lead to?

There are several expectations from the people we love. And because we have expectations, when these expectations are not meant, we experience abhorrence. This is generally what attachment leads to.

When we have attachment towards anything or anyone, we have expectations.
If our expectations are met, we are happy. But if the expectation is not met, then we are disappointed, which eventually leads to abhorrence. Thus, our emotions keep fluctuating, depending on the situation.

The intensity of our emotions is related to the level of attachment we have for that person or circumstance. Higher the attachment, higher the reaction!
For example, parents are naturally very deeply attached to their children. And this attachment increases all the more when their children do things according to their wish, making them feel happy and proud.

However, when children do not listen to their parents or fulfil their expectations, they get angry and upset. This is because while parents do everything for their children, in turn, they expect their children to at least listen to them and respect them.

But where there exists the virtue of equanimity, one is able to maintain the inner balance, both at the time when the circumstance of attachment arises and also at the time when the situation of hatred comes up. Hence, when we maintain equanimity, consequently, there is inner peace and harmony with everyone, and in all circumstances.

The virtue of Equanimity leads to Liberation!
Also, maintaining equanimity leads to liberation, which is the ultimate purpose of human life. Not maintaining equanimity is the reason why the worldly life, comprising of suffering, misery and bondage, continues, and maintaining equanimity, as we just said, leads to liberation.

The pure Soul is indeed the pure Soul, it is free from attachment and abhorrence (Vitaraag - detached). However, the prakruti (the non-Self i.e. the body complex) is with attachment and abhorrence (raag-dwesh). Prakruti is the one that needs to become free of attachment and abhorrence. So that the prakruti becomes free from attachment and abhorrence, the Knowledge about the pure Soul has to be realised. – Param Pujya Dada Bhagwan.

The only way to be able to maintain equanimity is by attaining Self-realisation.
When you are Self-realised, you have the awareness that ‘I am a Pure Soul. The non-self body-complex is the one that experiences emotions of attachment and abhorrence, whereas the pure Soul is always in the state of equanimity.’ Thus, you learn to remain detached from the non-self body-complex and remain more and more in the awareness of the state of the Self.

In the state of the Self, one is never attached to anyone or anything. The Self only Sees and Knows what the non-self complex is experiencing, it never becomes one with it.

To know more: https://www.dadabhagwan.org/self-realization/

Author's Bio: 

Ambalal M. Patel was a civil contractor by profession. In June 1958, spontaneous Self-Realization occurred within Ambalal M. Patel. From this point on, Ambalal became a Gnani Purush, and the Lord that manifest within him became known as Dada Bhagwan. A Gnani Purush is One who has realized the Self and is able help others do the same. Param Pujya Dada Bhagwan used to go from town to town and country-to-country to give satsang (spiritual discourse) and impart the knowledge of the Self, as well as knowledge of harmonious worldly interactions to everyone who came to meet him. This spiritual science, known as Akram Vignan, is the step-less path to Self-realization.