The psychic ability of empathy is defined by the dictionary as being the direct identification with, understanding of, and vicarious experience of another person's situation, feelings, and motives. Literally an empath can feel what you are feeling. Not only that but they will experience it to the same degree that you do.
Being an empath can be a very onerous task. Imagine meeting someone who has just lost a loved one and feeling what they feel. Don't mistake this gift for sympathy. We nearly all feel sympathy for someone in that position but an empath will experience those feelings as if they too had just lost a loved one. The feelings will be every bit as real.
This is not a gift that most would associate with the word psychic but many psychics will be an empath to a degree.
In the same way that it is necessary (perhaps even more so) for a clairsentient to take precautions to protect themselves it is absolutely vital for an empath to do so. They can literally be drained physically and emotionally as a result of their gift.