Empathy is a word that means that someone is able to share or understand the emotions and feelings of another person. Someone may need to have a certain amount of empathy before they are able to feel compassion. The word was coined in 1909 by the English psychologist Edward.B. Titchener.

Definitions 
Empathy is an ability with many different definitions. They cover a wide spectrum, ranging from caring for other people and having a desire to help them, to experiencing emotions that match another person's emotions, to knowing what the other person is thinking or feeling, to blurring the line between self and other. Below are definitions of empathy:

 Daniel Batson: "A motivation oriented towards the other".
 D.M. Berger: "The capacity to know emotionally what another is experiencing from within the frame of reference of that other person, the capacity to sample the feelings of another or to put one's self in another's shoes".
 Jean Decety: "A sense of similarity in feelings experienced by the self and the other, without confusion between the two individuals".
 Frans de Waal: "The capacity to (a) be affected by and share the emotional state of another, (b) assess the reasons for the other’s state, and (c) identify with the other, adopting his or her perspective. This definition extends beyond what exists in many animals, but the term “empathy” … applies even if only criterion (a) is met".
 Nancy Eisenberg: "An affective response that stems from the apprehension or comprehension of another's emotional state or condition, and that is similar to what the other person is feeling or would be expected to feel".
 Alvin Goldman: "The ability to put oneself into the mental shoes of another person to understand her emotions and feelings".
 Heinz Kohut: "Empathy is the capacity to think and feel oneself into the inner life of another person".
 Harry Prosen: "an emotional understanding which allows one as a therapist to resonate with ones patients in depth emotionally, so that it influences the therapeutic approach and alliance with the patient".
Carl Rogers: To perceive the internal frame of reference of another with accuracy and with the emotional components and meanings which pertain thereto as if one were the person, but without ever losing the "as if" condition. Thus, it means to sense the hurt or the pleasure of another as he senses it and to perceive the causes thereof as he perceives them, but without ever losing the recognition that it is as if I were hurt or pleased and so forth.
Marshall Rosenberg: "Empathic connection is an understanding of the heart in which we see the beauty in the other person, the divine energy in the other person, the life that's alive in them".
Roy Schafer: "Empathy involves the inner experience of sharing in and comprehending the momentary psychological state of another person".
Wynn Schwartz: "We recognize others as empathic when we feel that they have accurately acted on or somehow acknowledged in stated or unstated fashion our values or motivations, our knowledge, and our skills or competence, but especially as they appear to recognize the significance of our actions in a manner that we can tolerate their being recognized".
Edith Stein: "Empathy is the experience of foreign consciousness in general".
Simon Baron-Cohen 200): "Empathy is about spontaneously and naturally tuning into the other person's thoughts and feelings, whatever these might be [...]There are two major elements to empathy. The first is the cognitive component: Understanding the others feelings and the ability to take their perspective [...] the second element to empathy is the affective component. This is an observer's appropriate emotional response to another person's emotional state".
Khen Lampert (2005): "[Empathy] is what happens to us when we leave our own bodies...and find ourselves either momentarily or for a longer period of time in the mind of the other. We observe reality through her eyes, feel her emotions, share in her pain".

Lack of empathy 
Empathy is found in many, perhaps all, mammals, and may be essential part of our specie. It does help the group as well as the individual. Lack of empathy is found in various types of mental disorder, such as psychopathy, antisocial personality disorder, narcissistic personality disorder and sadistic personality disorder.

References

Other websites 
 Empathy Definitions by Edwin Rutsch from the  Center for Building a Culture of Empathy.
 Mirrored emotion by Jean Decety from the University of Chicago.
 Empathy and the brain by Gwen Dewar published in Parenting Science.
 Empathic listening skills How to listen so others will feel heard, or listening first aid (University of California).
 Study: People literally feel pain of others - mirror-touch synesthesia Live Science, 17 June 2007.

Emotions
Psychology
Life skills