"If there is one secret of success, it lies in the ability to get the other person's point of view and see things from that person's angle as well as you own." What does it mean?

It means one of the secrets of success is the ability to understand people well. Which could also translate to having a high EQ (Emotional Quotient).

Explanation:

The success being talked about here is not only Financial but also Individual/Personal success (i.e when a person is generally happy and feels fulfilled).

Seeing things from the other person's view point helps you to understand why he/she behaves thinks and reacts to things the way they do. When you understand other people's emotions as well as your own, you : are able to make better, objective and intentional decisions in every aspect of your life, whether personal or at the workplace; become more confident; and have healthier relationships. This brings all-round success.