It's useful to understand the mechanisms, it helps you to understand both what it can do, and its limitations. E.g. they can only mirror the parts they see or talk about. The parts of yourself that you hide away will be lost from their imperfect model.

For more info, it generally falls under "mirror neurons". They help us empathise with others. E.g. when we smile, certain mirror neurons start firing. When we see someone smile, the same ones fire. We feel the appropriate emotions because of this. They also fire preemptively. E.g. when you hear your mother yelling about the mess, even though you've lived alone for a decade.