Some good writeups about Tai Chi, but they're still missing the essence. "Tai" means supreme. Chi has is often translated as breath or energy or spirit. In fact, Chi represents the Chinese concept of the "spiritual energy" that constitutes the universe. Instead of believing that the world was made of matter, they believed the world was made of Chi--energy that not only made up everything, but also flowed through everything. (Use The Force, Luke.) So Tai Chi can be translated "supreme power". And yes, as themusic noted, Tai Chi is in fact a martial art. It always was and always will be a way of fighting.
Masukomi is correct in most of his writeup except for the part about redirecting your opponent's chi to use it against him. The true nature of Tai Chi combat is to merge your chi with your opponent's, "helping him to go where he wanted to go." An example is when an opponent punches you help his arm go forward by adding your own energy (chi) to his, causing his head to whiplash. His natural reaction at this point will be to try to stop and go back, so you again merge your chi with his, sending him flying across the room. Thus Tai Chi is a soft martial art, to the practitioner, but to the one on the receiving end, Tai Chi is a very very hard martial art.
A common misconception about Tai Chi it is that is slow. True, it is often practiced slowly, but there is nothing slow about it. Energy is like a kitten, afraid of fast movements, but as kittens grow, they become less skittish and can tolerate sudden and fast movements. Thus to develop power and energy, Tai Chi must be practiced slowly, but as energy is developed and grows up, the Tai Chi master can move quickly and maintain his power.
Tai Chi is also not necessarily "round". The same form can be done square or round. Both have their purposes, and both should be practiced.
And finally for some Tai Chi in movies, see Jet Li's Tai Chi Master (distributed in the United States under the name Twin Warriors). It is about the founder of Tai Chi, Chang Sang Feng. Incidentally, Jet Li practices Wu Shu, which is a combination of most of the major Chinese Martial Arts.
Of course the best Tai Chi master in film today is Bolo Yeung who has bigger breasts than most women. He played the infamous Chong Li in Bloodsport and has acted in some fifty kung fu flicks, including Bruce Lee's Enter the Dragon.