This is often one of the hardest concepts for the western mind to grasp.
The character for qi in Chinese is a grain of rice, beneath vapor.
Another way of understanding it is the air you breathe plus the food you eat.
One instructor I had at school said a good explanation for the scientific mind is to describe it as ATP.
My understanding is that qi is the basis for your being. One of my mentors used to say when you were born you received 3 treasures: Jing, Qi, and Shen.
If Shen is your mind, and Jing is your genetic makeup (effectively your body), Qi is the connection that resides between the two. I know this is a bit of an esoteric description, but if you understand that your qi leads the processes that happen in your body, perhaps it is a little easier to understand why it is so important in your treatment.