To empathize is to understand someone else’s feelings or problems from the inside, especially because you have had something like it — or can imagine it clearly. “I can empathize with that” is a very common, warm sentence. You empathize with a person. Teachers, nurses, and friends use it; it is not slang, but it is also not stiff. British spelling is often empathise. Compare sympathize: that is closer to “I feel sorry for you” or “I stand with you.” Empathize is “I get how this feels.” Though actually, people sometimes stretch it to mean little more than “I hear you,” even when they have not really taken the feeling in.