It can mean a lot of things.

Most of what they do is observe what you are doing and objectively send it back to you, like a mirror. It helps build your sense of who you are.

Some go as far to literally sit the way you sit, and even dress the way you dress.

Most commonly, they will take wha you just said to them, and repeat it back to you in their own words. This not only makes sure they understood you correctly, but make you feel like they truly heard what you said.