The term Qi (chi) literally means "breath". It is an energy considered to circulate throughout the body. It can be cultivated through meditation and qigong (lit "breath exercise") and the practice of internal martial arts which are all about Qi.
Does it really exist? I happen to think so but not in the somewhat supernatural manner it is so often presented in. Rather Qi flows from having certain things in harmony - Yi (the reasoning mind) and Shen (the spirit). when these are properly harmonised then Qi flows properly and you will find movements, especially in martial arts, easier. Qi doesn't really let you do anything superhuman.
Can it be used to give blows more power? I suppose so. When motion is easier and balanced technique is improved. Then there is fajin which is a way of utilising the harmony of Yi, Shen, and Qi to produce Jin ("energy"). In arts like XingYi, Taiji, and Bagua Jin and Fa jin are important aspects that are goals for parts of the training process.
It would be nice to walk on water, leap over trees, and punch holes in walls though.