Sympathy is feeling sorrow or pity for someone else's situation, often from a distance, without necessarily understanding their emotions. Empathy is deeply understanding and sharing another person's feelings, as if stepping into their shoes. Sympathy says, "I feel sorry for you," while empathy says, "I feel with you."
Essentially empathy is assuming you can know what the other person is going through, which you can't. If you sympathize you can help them. If you empathize you will be misled and can make things worse.