The short answer is: a 300+ year old martial art that is greatly beneficial to the practitioners’ health.
The correct name for tai chi as a martial art — which is what we’re solely about here — should be tai chi boxing. Tai chi in Chinese means supreme ultimate literally, and is a term used in Chinese philosophy to describe what some believe to be the beginning state of the universe: a state of nothing but energy mass. Out of this energy mass comes the two states of yin and yang, which further develop into states of four, eight, etc., and eventually into the complex world that we’re in right now.
Note that the major relevance of tai chi as a philosophical concept and tai chi as a martial art is probably only in that tai chi boxing is trained around the concept of yin and yang. In general, bones are yang and muscles are yin. In addition, the practitioner should know very clearly which parts of his body is yang and which part is yin throughout the movement, which changes dynamically throughout.