Qigong (pronounced "chi gung") means to cultivate energy and is practised to improve physical, emotional and mental health, increase energy, vitality and overall well-being. It can loosely be translated as the attainment of Qi.
Qi is the life force or vital energy which flows through all things in the universe and is essential for health. Gong is the accomplishment or skill which is attained through hard work.
These exercises are fantastic for overall health and can be done without a warm up whenever you have time. Like Tai Chi, the movements are at once very simple but very deep. Practising them will help improve your understanding of both and gain a deeper awareness of how your body is connected.
Tai Chi can be seen as part of two long-established systems of exercise in China known as Qigong and Wushu (Martial Arts). Qigong optimises the flow of Qi through the body in the same way that Tai Chi does. Tai Chi is a system of Qigong and a Martial art, whereas Qigong is only used to optimise Qi flow in the body.
People spell it different ways: Chi or Qi means "energy" and Gung, Kung, Gong or Kong means "method of cultivation". It's also sometimes referred to as Dao Yin, so don't get confused as it's all the same thing, just translated into English characters by different people.