What is Tai Chi ?

Tai literally means 'Supreme' or 'Big', Chi here means 'Ultimate' or 'Best' while the character Chuan denotes a fist.
A very crude translation of the whole phrase might be 'Supreme Ultimate Fist'.

Actually, tai chi/supreme ultimate refers to an old Chinese philosophical concept regarding the creation of the universe. Briefly, this was that out of chaos and nothingness, an event - tai chi - gave rise to yin and yang, the complementary opposites which make up the world in varying amounts. Yin alludes to softness, female, darkness, earth, while yang alludes to hardness, male and brightness and heaven. In the place or state of tai chi, the two co-exist, not in opposition, but in balanced harmony, dynamically cycling from one to the other.

The fist character denotes that this is a martial art or exercise system that founded upon the tai chi concept.

But tai chi chuan is more than a martial art. Just as some people work out by doing boxercise or tae-bo, but never want to get in the ring, wu style tai chi allows you to learn internal technology that can greatly benefit your health without having to be a martial artist.
The principle of tai chi practice is to be able to change from yin to yang in a fluid relaxed manner.

What is a 'Wu style'?

A 'Wu' is a person's name, not a thing.
Wu Chien Chuan is the name of the person who created and founded this tai chi style. His own father was a top student of Yang Lu Chan, the man who first taught tai chi publicly in 19th century China.
His style is characterised by smaller stances than the more commonly known Yang style of tai chi chuan. This places less physical demands on the body and is a very useful style for those recovering from injury.

For more info on this style, with picture of the founders, see this page on Frank Allen's web-site, the Wu Tang PCA.