If you google "matching and mirroring" you will find page after page of articles and videos mostly explaining that the practice of matching and mirroring someone else's physiology or language will allow you to build rapport.
I am no longer sure that's entirely accurate.
Here's what I have come to believe after almost ten years of teaching NLP and observing rapport as it develops: mirroring and matching is a sign of rapport. Working at mirroring and matching (doing it deliberately) signals that you are interested in entering into rapport. Paying attention to someone else is always a good way to start a relationship.
The most productive way to think about matching and mirroring is to notice that it gives you the ability to be much more perceptive about the person with whom you want to connect. When you are matching them, you do not have to rely on external observation of their state. You can notice how you change as you move into their movements, mannerisms and vocal patterns. You can assume that what you feel while mirroring them is related to what they are experiencing as they relate to you. This gives you an edge in noticing, acknowledging and predicting their experience of your connection.
The next most productive way to think about matching and mirroring is to notice when someone is matching you. This is confirmation that they're listening and connected: you have permission to say something interesting or to take a step in the expectation that they will follow. No matching? You need to pay more attention to them. When they're ready to connect with you, you'll see it in the way they match your behaviour or language.
It's true that matching and mirroring offer powerful tools for making stronger connections. Used wisely, they allow you to observe more accurately and to make better predictions about when someone is likely to follow your lead. The keys to remember are: check your state before you connect, so you'll know what changes when you mirror; offer someone your real attention so they have a reason to connect; notice what changes when you mirror; and notice when they're mirroring you.