In my opinion the the ability to sense what others are in such as happy situations or sad.
From the web here is a very clear definition:

feel·ing (flng)
n.
1.
a. The sensation involving perception by touch.
b. A sensation experienced through touch.
c. A physical sensation: a feeling of warmth.
2. An affective state of consciousness, such as that resulting from emotions, sentiments, or desires: experienced a feeling of excitement.
3. An awareness or impression: He had the feeling that he was being followed.
4.
a. An emotional state or disposition; an emotion: expressed deep feeling.
b. A tender emotion; a fondness.
5.
a. Capacity to experience the higher emotions; sensitivity; sensibility: a man of feeling.
b. feelings Susceptibility to emotional response; sensibilities: The child's feelings are easily hurt.
6. Opinion based more on emotion than on reason; sentiment.
7. A general impression conveyed by a person, place, or thing: The stuffy air gave one the feeling of being in a tomb.
8.
a. Appreciative regard or understanding: a feeling for propriety.
b. Intuitive awareness or aptitude; a feel: has a feeling for language.
adj.
1. Having the ability to react or feel emotionally; sentient; sensitive.
2. Easily moved emotionally; sympathetic: a feeling heart.
3. Expressive of sensibility or emotion: a feeling glance.

--------------------------------------------------------------------------------

feeling·ly adv.
Synonyms: feeling, emotion, passion, sentiment
These nouns refer to complex and usually strong subjective human response. Although feeling and emotion are sometimes interchangeable, feeling is the more general and neutral: "Poetry is the spontaneous overflow of powerful feelings: it takes its origin from emotion recollected in tranquillity" (William Wordsworth).
Emotion often implies the presence of excitement or agitation: "Poetry is not a turning loose of emotion, but an escape from emotion" (T.S. Eliot).
Passion is intense, compelling emotion: "They seemed like ungoverned children inflamed with the fiercest passions of men" (Francis Parkman).
Sentiment often applies to a thought or opinion arising from or influenced by emotion: We expressed our sentiments about the government's policies.
The word can also refer to delicate, sensitive, or higher or more refined feelings: "The mystic reverence, the religious allegiance, which are essential to a true monarchy, are imaginative sentiments that no legislature can manufacture in any people" (Walter Bagehot). See Also Synonyms at opinion.
source:
http://www.thefreedictionary.com/feeling