Empathy is the magical ability to experience the emotions of others without direct contact with them. This is Phoebe Halliwell's second and last active power. This remains one of her powers until she loses her active magic for abusing her abilities. Phoebe says that it must have grown from her power of premonition. At first, Phoebe was able to control her empathy to an extent, allowing her to to mimic the powers of other magical beings by tapping into their emotional triggers, but she was unable to control the inward flow of emotions and soon barricaded herself in the Manor's basement in order to block off the emotions of the world around her. Soon, her sisters and Chris took a potion in order to block her from reading their emotions, effectively keeping her out of their heads.
Eventually, she was able to control the flow of the emotions and could actively block the emotions that others were subconsciously sending to her.
Prue temporarily gained the power of empathy and was unable to control it and was constantly taking in the emotions of the surrounding San Francisco area. With the help of the father that originally had the power, Prue was able to get a grip on the incoming emotions and used them to help her battle the demon Vinceres. With the greater amount of emotions that Prue had taken on, she was able to increase her telekinetic powers to a far greater level, allowing her super strength and a higher form of agility. By focusing human pain into her astral self and then invading Vinceres's body, she was able to literally rip his body apart.
Magical beings that are born with this power are called Empaths. They usually grow-up with the ability and become psyciatrists, priests, doctors and so on and are blessed with immortality. One could think of them as whitlighters but with way less powers. Empaths are normally always beings of light because demons and warlocks can't feel many emotions aside from pride anger and hate and therefore they can't handle the power of human emotion. In the show natural born Empaths are also shown immortal however it is unclear whether or not a witch who gains the power of empathy as a natural power advancement (such as is the case with Phoebe) is also or becomes immortal too though it seems unlikely.