Tai Chi
I am NOT specialized in Tai Chi. For accurate descriptions of exercises or moves, consult verifiable sources.
Tai Chi or Taijiquan literally translates to 'Great Ultimate' and is a Chinese martial art and form of meditation. Key characteristics are slow movements, deep breathing and focus. The main goal of Tai Chi is to balance the energy of your body, otherwise known as qi, improving your general health, and harmonizing with the flow of the universe, like all forms of Taoist meditation.
Qigong
Qigong is a system of body movements that aim to promote one's internal health, i.e. breathing, guts, bones, etc. It was conceived around 2700-2600 BCE by the legendary Yellow Emperor. It's been used in China to combat various diseases for thousands of years. Tai Chi holds various principles of Qigong, but note that both are different systems (with Qigong's moves being generally easy to learn for beginners).
Patience
Tai Chi makes use of slow, gentle movements unlike other martials arts like Kung Fu which are more fast paced. This allows for deliberate moves, not relying on brute force or assertion. Tai Chi can be considered to be hard to master due to the requirement for 'full-body integration', which needs practitioners to maintain a strong, upright posture without slouching.
Self-defense
Tai Chi oftentimes doesn't require strength to defend oneself. Mechanics of the body are your friend, for example when someone pushes your chest, you can bend your elbows, relax your shoulders and align your forearm diagonally, creating the Peng Jin (or Unbreakable Arm) which causes the force to disperse over your entire body instead of your muscles resisting.
Movements
Tai Chi's moves are often long and choreographed sequences and take generally long to master forms. Classes were originally martial-oriented, though moves now also are for phyiscal and mental health.
Breath Control
Being able to breathe in and out deeply is essential to mastering Tai Chi. Why? Because breath act like guidance for your energy (qi). Deep and slow breaths help move qi, while shallow breathing causes the flow of energy to block. Controlled breathing ensures your dantian (energy center of qi) is engaged, which helps ground your posture and prevent stiffness.