What is Tai Chi Chuan and where did it begin?

Tai Chi Chuan means the Supreme or Grand Ultimate Boxing (Chuan also meaning fist and control.)
A primary objective of the system is achieving self-discipline through practice and mastery of Tai Chi's forms including the Standard Form, the Round Form, Broad Sword and Spear. 

Achieving self discipline manifests itself as  Self Preservation (good health), Self-Expresssion (art) and Self Defense (martial skill).