Tai Chi Chuan is certainly great for mindfulness and stress release, but it also has been an important martial art since its very beginnings (Tai Chi Chuan means “great ultimate fist”). Some even consider it the “best” martial art, because it also works with internal work and mediation. This makes it very powerful: Every single move has a health and a martial arts benefit.
Secondly, doing applications increases our ability to relax, be mindful, and remain in the flow. It is very easy to be all meditative and ‘cool’ when we stand in a protected room and nobody bothers us. However, when we have a Tai Chi-partner who starts walking towards us and tries to give us a slow, controlled ‘push’, it is much harder to stay calm and relaxed. Our partner work is a test and a good practice of our ability to remain in a mindful and meditative state even when we feel under pressure. We don't 'fight' incoming pressure, but we deflect it in a big circular move... a very peaceful way of handling it.
This is what we need in real life outside of the training hall: Using our Tai Chi skills to remain calm, balanced and relaxed in every situation. All we do in the class is of course very safe and practiced in slow-motion, and it happens in a friendly atmosphere.