The Tai chi movements (tai chi postures) teach us many things. On a Physical level, they teach us about balance, timing, coordination etc. Building a strong body that is needed for a healthy life. Also by strengthening the body in this way, it enables us to then be more relaxed in our movement, so that in the higher levels of training we can achieve higher Qi Flow.
When we first start training, everyone learns to do the movements in the same way, as they were designed in a way to be physically balanced, thus balancing out any internal problems etc.
Through our training, the movements teach us how to become in touch with our Qi, linking the external movement with the internal Qi flow in the body. This is why practitioners at the highest levels all look slightly different doing their form, as they're doing what their Qi wants to do, not what they've been told to do. Though it is very important to do the set way of movement in the beginning, as if your Qi is far to Yin for instance, then you don't want to do your form in harmony with that, as then you will never balance out. The set way of doing the movements have a balance of Yin and Yang.
Each posture in Tai Chi has a deadly martial application, and teaches us about reflexive street fighting, unlike some styles that teach competition fighting, which are two very different things. Through the internal side of things, they teach us how to concentrate our intent to where the strike is etc, putting your whole bodies power in one spot.
The movements activate the energy meridians in the body, through stretching and palm to palm activation. Opening up the channels, clearing any blockages etc.