Emotional Intelligence can be summarized as possessing the skills or ability to detect, identify, learn from, and respond to various emotions in yourself and those around you.
Having this ability is essential for most of the aspects of our lives. We need this ability for jobs, family, social lives, and just the general public surrounding us. For example, a salesman would need to recognize what kind of emotion his possible buyer is feeling so that he can say the right thing in order to turn that person into a satisfied customer.
I firmly believe that having this skill fine tuned can drastically change someones life. It could be anything from performing well at work and climbing up the ranks to reading an opponent in a high stakes poker hand. However, recognizing certain emotions in yourself is just as important. We need to know when we are angry or depressed so that we do not do something regrettable out of pure emotion.
As of right now, emotional intelligence was needed the most in my life during my days playing high school football. It seemed like my football coach had 10 very different personalities. Some days he would make jokes with us and let us watch TV in his office and then other days he would make other players do push-ups for not calling him "sir." I tended to steer clear of him if I saw him do something like kicking over a chair that indicated he was not in a good mood.