The proliferation of Tai Chi (Taiji) and the Internet has resulted in numerous viewpoints and explanations of the basic meaning of Tai Chi. Originally, Tai Chi came from the I-Ching, which is one of the oldest books in ancient China. According to the I-Ching, “Tai Chi gives birth to two Yi.” The words “Tai Chi” literally means the “ultimate”, and the two “Yi” represents the “Ying” and “Yang.”
In Chinese culture, Tai Chi is refered to as Tai Chi Chuan. Although the literal meaning of “Chuan” is “fist,” the actual meaning is martial arts. Hence, Tai Chi is the martial art that concentrates on the study and application of both the Ying and Yang. However, even though Tai Chi is a deadly martial art, it is a way of life. “The ultimate meaning of Tai Chi practice is to expand your life span without aging while maintaining a youthful body at the same time.” (The Tai Chi Classics)
Here are some common definitions of Tai Chi that I have found in the Internet.
“Also Known as TAI CHI CH’UAN, and is part of the Tai Chi Ch’uan System, which, originally, was a formidable martial art operating on several levels of awareness. It embodies Taoist Philosophy, and accordingly is extremely beneficial to good health. Tai Chi is a comprehensive series of gentle physical movements, and breathing techniques, with mental and spiritual intent, which allows you to experience a meditative state. It is calming and rejuvenating, and assists the body and mind to maintain balance, and exercises the body, mind and spirit, together with the internal organs. It includes both the inner and outer expressions of the body and mind. Here we are able to balance the Yin and Yang life force energy of Chi. In this way this system develops the ability to balance the “yielding and attacking” aspects in martial art combat. It has also been such a major influence in all the martial arts we see today.”
http://healersoftheworld.com/glossary/glossaryR-U.html
“A Chinese system of physical exercises designed especially for self-defense and meditation.”
“Chinese system of slow meditative physical exercise designed for relaxation and balance and health”
http://www.thefreedictionary.com/tai%20chi
“Tai chi chuan is a style of kung fu that consists of fluid, graceful standing movements. Often called the "moving meditation," it emphasizes softness over hardness, a concern with things internal rather than external, yielding over confrontation.”
http://health.discovery.com/centers/nutritionfitness/
fitness/articles/techniques/taichi/taichi.html