Judgment, Stereotyping, and Empathic Compassion

I am somewhat curious, following an answer to a previous question of mine, as to why understanding a person's background might inhibit judging them in a stereotypical way. I perceived this in my practice and I have found it somewhat effective in my own case, but I am unsure why this is so. I feel as if such awareness of background is a bit superfluous, yet then again I feel empathy is less frequent when we don't understand a person's motivations. Consequently, I wonder: 1. Why is understanding motivations effective against judging others according to Buddhism? 2. How can this idea be best applied in meditation? For example, how would meditating on the causes of suffering--to arouse compassion--be achieved? Thank you