Empathy is the capacity to share feelings of others.
Sharing the feelings of others can be an ability or an inability. In extreme cases a person's own sense of identity may be damaged, and such an empath may involuntarily take on the feelings of others.
I mention this because we all do this to some degree - the feelings and reality of other human beings around us influences in one way or another.
Psychic empathy is the ability to assume the feelings of others at will. To be able to do so, a psychic empath must first master his or her own feelings. It can be useful to think of our own thoughts as tools, and it can also be useful to think of our feelings as tools as well.
Emotional discipline allows the psychic to be unphased about emotional ebbs and flows. Understanding the thoughts of someone tells us about their more conscious, rational side. Understanding and empathizing with the feelings of someone tells us more about their subconscious, irrational side.
In other words, psychic empathy is about putting yourself in different shoes - and it's good if you can take of the shoe you already have on before puting on a new one.