T’ai Chi (properly pronounced tie-jee, but often heard as tie-chee in the West) is an ancient martial art focusing on smooth, slow movements that cultivate inward focus and free energy flow. T'ai Chi — compared to fighting arts — wants you to use your mind to focus and move. Some people even call T’ai Chi a moving meditation. T’ai Chi is rooted in the Taoist (pronounced dow-ist) philosophy of harmonious living.
You may hear the term mind-body fitness to describe movement forms like T’ai Chi, as well as other stuff like yoga. That term is basically interchangeable with the descriptor mindful. Although the definition of mindful movement is changing practically daily, one can loosely describe it as a “physical exercise executed with a profound inwardly directed focus.” In other words, you use your muscles, but you also engage your mind.
T’ai Chi is a member of the martial arts family, just like all the other practices in which you engage in flamboyant, teeth-kicking combat. They all belong to the family called Wushu, which basically means “martial art” or traditional self-defense activities practiced with or without weapons. Other Wushu forms date back much further than T’ai Chi. If you observe the movements of those participating in a T'ai Chi class (for example, the circling, torso-turning, hand-pushing, and leg lifting), you can to see the resemblance to fighting martial arts.
Although some people practice T’ai Chi to perfect these movements (called forms), to gain inner strength, and to improve their combative martial arts, most people in the West practice T’ai Chi for the peace, inner calm, focus, energy, balance, stress relief, and body control.