Compassion feels with others' Dukkha. Equanimity understands our limited power to end it, understands that there are many things beyond our power to control. By understanding the "Three Characteristics of Existence": Impermanence, Dukkha and Anatta -- we understand that all conditioned things are impermanent, and in being impermanent they are unsatisfactory and not within our power to totally control. So, understanding our limited power to control things and to end Dukkha - especially somebody else's, or the world's - we have humility, and balance our compassion and opening to Dukkha with the wisdom to know what we can, and what we cannot change.
In every day life, this balance is almost essential, as we come upon relationships with others where we may, as we develop more compassion, become quite sensitive to other people's suffering. We may even know what causes it, but we also realize that other people have to give us the consent to help them. Even if they've given us consent to influence them, they may have limited power to follow what we suggest, depending on their Kamma.
Understanding that everybody is "the owner of their own Kamma", helps to give us more balance as we walk through life. To understand that some people have the good Kamma to be able to understand, and some people do not. Some people have the power to take their understanding into practice and some people do not. So it prevents us from falling into grief, because we start to accept that Dukkha does exist in the world. This is the first Noble Truth, Dukkha does exist. Can we accept it? Can we accept that the world is not perfect, and as we would like it to be? Quite difficult at times but non-acceptance only takes us into more Dukkha. So we need to develop the courage and strength to accept life as it is, and see what we can and cannot change.
In our every day life, as we view others and ourselves, sometimes we have the capacity to change and help, and sometimes we do not. Can we accept that we cannot make the world the way would like it to be, or others as we would like them to be? But, can we also remember we do have the power to prevent ourselves suffering with it.