Tai Chi is a form of martial art. Its premise is that if you're balanced, you can overcome an opponent of (practically) any size and/or strength. This is because, as an opponent attacks, s/he is off-balance during the attack. You can overcome the attack by deflecting it, and using the opponent's lack of balance against him/her.

The movements are slow and fluid, as stated elsewhere in this thread. They are designed to release energy within the body, to make it flow smoothly, thereby raising awareness and energizing reflexes. When I studied it (casually) many decades ago, the point of all the movements were to remaim balanced throughout the movements. The energy release and channeling aspects are the parts that are relaxing; nonetheless, your heart rate does increase, and you can break a sweat. (I did, anyway).

When studied as a martial art, the movements become larger, faster, and more targetted to defending against an attacker. I was told that, as a martial art, Tai Chi is strictly defensive; since the act of attacking necessarily throws you off balance, attacking is contrary to the premis of the art. (However, I'm no expert on this, so anyone with greater knowledge about this should feel free to correct and educate me.)