I always describe empathy as having three distinct parts.
Cognitive empathy: understanding how someone sees a situation. “I get your perspective,” or “I understand how you are thinking about this.”
Emotional empathy: feeling what someone else feels, in part through mirror neurons and other structures of the social brain. This is what creates rapport and genuine connection.
Empathic concern: caring – for example, sensing that someone needs help and being moved to act on it. This is where empathy can become compassion.
Here’s something to think about: you can have strong cognitive empathy without emotional empathy or empathic concern. This means you can read people well but not care about them.