How Do We Define Empathy?

Empathy is Understanding and entering into another's feelings.
Sympathy is Sharing the feelings of others (especially feelings of sorrow or anguish)
apathy is An absence of emotion or enthusiasm.

Empathy is the capability to share and understand another's emotions and feelings. It is often characterized as the ability to "put oneself into another's shoes," Empathy does not necessarily imply compassion, sympathy, or empathic concern because this capacity can be present in context of compassionate or cruel behavior.

For a clearer picture about it have a look at: en.wikipedia.org

Identification with and understanding of another's situation, feelings, and motives.

"Empathy" is being able to feel the emotions of others based on a common understanding. For example, two people who have each lost a spouse, can feel empathy for each other because each understands what that is like. Conversely, "sympathy" means that you can commiserate with a person, even though you don't personally know what it is like to go through a certain situation. I can feel sympathy for those who suffered the effects of the 2004 tsunami, but not exactly empathy as I've never lived through that.