When people talk about the Tai Chi form, they are usually referring to the slow form. There are many other forms, such as the San-Sau fighting forms, and weapons forms etc.
Here I'm going to talk a bit about the slow forms. To the left you will see many detailed articles.
There are two versions of the long slow form, The Yang Lu-chan form, (Old form) and the Yang Cheng-fu form, (New form) The WTBA does not rate the shortened forms as proper Tai Chi, they are just a bunch of moves that look like Tai Chi, but have no depth.
The Tai Chi form is the mother of all the other forms, the weapons, the fighting forms etc, they are all based upon the long form. The Old form is the most balanced of all the forms, having mostly slow movements, but also a good amount of fast explosive martial moves, giving it a perfect balance of both yin and yang Qi, healing and martial qualities, as well as physically balanced, working the left and right sides of the body equally.
The new form however, was created to be made easier for older people or anyone not fit enough to perform the old form. And also by removing most of the martial intent from the form, the old masters could teach Tai Chi to outsiders with out them learning their family secrets. (Of course now a days everything is given out freely, because having the best fighting art is only useful for self defence, as today there are guns.) This means the form is in effect not balanced, you have to do it on both sides to balance the left and right of your body. As well as it is more yin than yang, and so if practicing this form, you need to balance it with the Small San-Sau.
How ever this is not to say it's not a good form. It does what t's meant to do. Better to do this form well, than the old form badly. Most people have to much yang in their life, through work and stress etc. So doing this form will only do good to your body. Giving you a better quality of life, relaxing your body and mind. Strengthening you body, gaining flexibility, balance and coordination etc. You only have to worry about the form making you to yin if you become very good at your Tai Chi, and are practicing many times per day. But if you're that into your training then you should probably try the old form by then.
The form is one of the main things that will help you to link your internal Qi in with you physical movement. This is the main thing we're trying to achieve in the art, for both the healing and martial side of things. You start off with a set way of doing the form, most people will do it the same in the beginning. In some cases an experienced teacher will teach a certain student a more yin or yang way of doing the form, suited to them.
After you become very proficient in the form, you will start to feel the energy in your body, and your form will change, linking to the flow of Qi in your body. Still doing the same moves, but in your own way. You must let this happen at its own pace, and take the guidance of your teacher. If you think you're ready and try to change your form with out feeling it, you will head down the wrong path and you training will go down hill.