The origin of Taijiquan is generally attributed to Chen Wangting, a highly respected general under the Ming Dynasty. When this was overthrown in 1644, he was unemployed and went back to his village (Chenjiagou).
He began to combine techniques from various martial arts with Chinese medicine and the teachings of Taoism.
"Tai" means very large, "ji" refers to the ridge beam of a gable roof, "quan" is the fist and thus points to the original meaning of Taijiquan as a martial art and for self-defense.
According to Taoist philosophy, the doctrine of yin and yang states that all polarities (e.g. active and passive, hard and soft, full and empty) belong together and form a living unity.
Yin and Yang achieve harmonious balance through continuous interplay, which shall be achieved through Taijiquan.
In order to make the health benefits of Taijiquan accessible to the general public, the Chinese government in Beijing released a shortened form in 1956, which is known as the Beijing form with 24 or 48 movement patterns today.
In the West, Taijiquan is often shortened to Tai Chi because the martial arts aspect (quan "fist") of Taijiquan is often put aside.
The shortened designation is therefore sometimes used on purpose.