"Taiji being born of Wuji, is mother of Yin and Yang.  In movement it differentiates; in stillness it consolidates." as the classics say.  That sounds interesting, but what is the meaning?

This passage comes a text called The Taijiquan Treatise by Wang Zongyue.  It follows Taoist (daoist) philosophy.  Wuji, the state before definition, can be thought of as nothingness.  All things are said to come from this original nothingness.  Taiji is the emergence and interplay between Yin and Yang, the first stage of creation.

The Taiji symbol is the easily identifiable black and white Yin/Yang 'fish.'  Yin is the soft, empty, female, dark etc..  Yang is the hard, full, male, light.  An easy exercise to understand how to define Yin and Yang is to stand on one leg.  The support leg is full, therefore Yang.  The suspended leg is empty, therefore Yin.  This is a very simplistic way to define these two aspects.  It helps a practicioner to understand that, like magnetic poles, Yang never leaves Yin and Yin never leaves Yang.

Taijiquan, aka Tai Chi Chuan, is a martial art that uses the philosophy of Taiji in its approach to self defense.  For example: when an opponent uses Yang (hard) energy you would respond with Yin (soft) energy.  If you were to respond to Yang energy with Yang energy, it would result in 'double weighting.'  This is a critical error and should be avoided.  The way to avoid being double weighted is developing the ability to distinguish empty and full (Yin and Yang).  The way one develops this ability is first through the solo forms to learn about oneself, and later, push hands to learn about your opponent.