The Tai Chi salute is based on history philosophy. In particular the history of the Red Faced General, Guan Kung, who is remembered for saying that across the universe we are all brothers and sisters, that is, we are all equal. It is said that when the Red Face General captured the emperor of the enemy he demonstrated his brotherhood by letting the emperor go rather than cutting his head off. In essence the salute symbolises aspects of Chinese culture, including respect, humility and politeness.
When you raise the hands, palms facing up to shoulder level, this symbolises and reminds us that we are all equal. A very polite and welcoming posture.
The right hand then forms a fist, the left hand is a palm. The right fist represents the Sun and the left palm the Moon. Together Sun and Moon represent happiness, brightness and prosperity. As you bring the two hands into the chest and press out again (still as palm and fist) you are wishing other people happiness.
Finally when the two hands return to the waist and you bow this is to show further respect and politeness to those present and acknowledge that life is a gift and that all life should be treasured. When the two hands press down it suggests peace.