One of the key things people notice about Tai chi is the fluid way the practitioner seems to move as they glide from one position to the next. This fluidity, although looking simple, is difficult to achieve and requires many hours of dedicated practice.
The fluidity of Tai Chi comes from the body working as one unit and not as a list of separate parts. This requires many things to be happening at the same time, often in different directions. It is possible to transfer the weight from one side to another and change leg positions, whilst at the same time twisting the body and rearranging the position of both hands and yet still breathing in a relaxed manner.
One example of this is Tai Chi walking in which you learn how to shift the weight forward as you step slowly in a very specific manner, while at the same time bringing the arms into various set positions, before shifting the weight backwards and preparing for the next step and changing the arm positions again. The process is repeated around the hall and the walking / stepping action becomes one continuous movement. The whole action looks lovely to see and feels great to do.
There are too many moves to generally learn this in one go, so the process has to be broken down in to smaller sections. Firstly the legs are taught with the correct flow of weight from one leg to another and the right alignment of the feet and hips. This movement has to be internalised and practiced until it can be carried out without hesitation, before the arms can be added and the movement completed.
The arm movements can also be learned and practiced on their own which also builds muscle memory and correct form, however when the two are practiced together the attention gets split and student has to do multiple things at once, which can cause confusion.
Slowness is therefore very important, allowing the legs and arms to work seemingly simultaneously, yet in reality with a split shift in focus that continually adjusts all the elements one after the other. In time the movements will become so normal that they will become fluid and continuous.
Like all worthwhile things in life this takes practice and patience.