Tai Chi Chuan has its origins in the martial arts. By practicing Tai Chi, you learn how to become aware of and work with your body's "chi", or vital energy. As you learn to sense your own chi, you then learn to sense and respond to another person's chi. By responding to an opponents potentially destructive chi energy (usually in the form of a kick or a punch), you can dissipate the energy or send it in a direction where it is no longer a danger. Understanding your chi requires both physical and mental training.
From a physical standpoint, Tai Chi strengthens all the muscles, especially the little ones that have been neglected by most people through most of their lives. The muscles must be relaxed to allow the chi to flow, yet they cannot relax if they are too weak to perform the necessary movements. Tai Chi also improves flexibility, especially in the hips. For the chi to flow, the body must be structurally aligned, which requires the joints to be able to open. Also, the muscles can be put under strain if the joints cannot open properly, and strain means a blockage of the chi. Finally, Tai Chi improves your balance. In order to move in a way that maintains the flow of chi AND allows you to respond to an opponents chi, you must be in balance.
From a mental standpoint, tai chi first opens your mind to an increased awareness of your own body. You learn what your body's strengths and weaknesses are, which teaches you what you need to improve. As you improve in tai chi, you then learn to become aware of the movements and chi of those around you, so you can respond if necessary. You also learn to focus as much as needed, yet not enough to waste your chi or distract you from the next thing you need to focus on.
In Chinese philosophy and medicine, there exists the concept of 'chi', a vital force that animates the body. One of the avowed aims of Tai Chi is to foster the circulation of this chi within the body, the belief being that by doing so the health and vitality of the person are enhanced. This chi circulates in patterns that are closely related to the nervous and vascular system and thus the notion is closely connected with that of the practice of acupuncture and other oriental healing arts. As it is often practiced in the west today, tai chi can be thought of as a moving form of yoga and meditation. There are a number of forms (yang, wu, chen, sung) which consist of a sequence of movements. The movements are originally derived from the martial arts (and perhaps even more ancestrally than that, from the natural movements of animals and birds) although the way they are performed in Tai Chi is slowly, softly and gracefully with smooth and even transitions between them.
Another aim of Tai Chi is to foster a calm and tranquil mind, focused on the precise execution of these exercises. Learning to do them correctly provides a practical avenue for learning about such things as balance, alignment, fine-scale motor control, rhythm of movement, the genesis of movement from the body's vital center, and so on. Thus the practice of Tai Chi can in some measure contribute to being able to better stand, walk, move, run, etc. in other spheres of life as well. Many practitioners notice benefits in terms of correcting poor postural, alignment or movement patterns which can contribute to tension or injury. Furthermore the meditative nature of the exercises is calming and relaxing in and of itself.
Tai Chi also has, particularly amongst eastern practitioners, a long connection with the I Ching Chinese system of divination. There are associations between the 8 basic I Ching trigrams plus the five elements of Chinese alchemy (metal, wood, fire, water and earth) with the thirteen basic postures of Tai Chi created by Chang San-feng. There are also other associations with the full 64 trigrams of the I Ching and other movements in the Tai Chi form.