In the beginning, the universe was a mess.

It was all mixed up.

Then everything divided into Yin and Yang.

As any number of people have pointed out- Taiqi is a mispelling but a common one here in the West. It should be:
TAI JI

TaiJi/taiqi as the exercise movement is fully known as Taijichuan.

So What is this Tai Qi symbol?

The Tai means the most and ji means ultimate. So this is the big thing.

Because the word Qi is so well known we in the West often used it with the Taiqi. Where I studied was known as the Taiqi Studio.

(Qi is a versatile and wide ranging word in Chinese - In the Western world it's meaning is under considerable scrutiny and debate. Often times we just use "energy" in the sense of "that guitar solo had a lot of energy" or even "I like that flower's energy". Scholars may scream but that's the best I can do right now.)