Taoist circular breathing is the smooth, seamless flow of chi through your nervous system during your inhales and exhales and most importantly during the change between them. It is an important quality of more advanced Taoist methods to link your breathing to physical movement and energy flow. Your breathing (inhales and exhales) should have no distinct starting or stopping points.  Taoist Circular breathing requires you to learn to mesh your breathing with your chi and nervous system so that they work together seamlessly. Successful circular breathing requires that you accomplish five tasks:  
— Become aware of the underlying quality or feeling of your nervous system as you breathe.
— Focus on the conjoined quality of your breath and nervous system as you  inhale and exhale.
— Find any gross gaps in your breathing, particularly at the changeover point between inhales and exhales.
— Train your awareness to become increasingly subtle and conscious of the microgaps in your breathing. Make your breaths go progressively sung (p. 114 of Opening the Energy Gates of the Body — see end of article).  As this occurs, become aware of even more subtle gaps that cause your nervous system to freeze momentarily during your practice. You will train until your nervous system becomes completely smooth and seamless and the difference between inhales and exhales disappears.
— The goal in the last phase of Taoist circular breathing is to directly find your chi. Having your breath be seamless and smooth can be the doorway to finding your chi; just as finding your chi is the doorway that can enable your breathing to become truly circular. They are interconnected and cannot be separated.

The task now is to make the jump from being only indirectly aware of your chi by its reflections in your breathing, nervous system and body (the goal of all the book Opening the Energy Gates of the Body), to becoming directly aware of chi as a separately-felt entity that empowers all movements in all your systems.

Awareness of subtleties and intentionality is a wonderful tool. As it becomes stronger and more refined it allows you to recognize and direct your energy in ways that otherwise would be impossible. As you practice more and your breathing becomes seamless, the barriers to being aware of chi dissipate. Gradually, with more and more breathing practice, your awareness will learn to fully penetrate your nervous system and become exceedingly familiar with it.

When this happens the last barriers to your breathing being fully circular will disappear. Eventually, your awareness will be able to recognize the underlying separate qualities of your breathing, nervous system and chi. You will become aware of the subtle current which interlinks all three. You will experience how your chi affects, is affected by and is the underlying force that joins and controls your nervous system and breathing.

Breathing with Chi

One day, as you focus on your breathing, the air coming in and out of your nose will seem to slow and then stop, while the insides of your abdomen and lungs will continue to move very powerfully. Even though you will be physically breathing well, it will seem as though your physical breath has gone totally silent and completely stopped and your body and mind have also spontaneously become silent.

An eerie silence and sense of incredibly expanded and empty space will arise within your body and mind. Suddenly you will find yourself silently breathing chi in and out. Then, this too will seem to slow to a stop. One day, during the circular breathing process your body and mind spontaneously will again become even more silent. Even though you will be physically breathing well, it will seem as though your breath has gone totally silent and completely stopped.

Within this space your sense of air movement will be gone but your organs will restart opening and closing (expanding and condensing) as though they have an independent will of their own. Now, instead of air being moved in and out of your nose, each expanding and condensing of your internal organs will bring in and expel something. This is chi.

After becoming experienced with this for a while, you will have gained the foundation to gradually become able to directly move chi anywhere in your body by conscious intent alone, using all the components of neigong.

From http://www.energyarts.com/advanced-breathing-techniques

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Page 114 Opening the Energy Gates of the Body : (A free pdf of this is at https://s3.amazonaws.com/free-giveaways/Energy_Gates_Chpt_7_8.pdf

In China, qigong and tai chi masters use the word sung when they want their students to feel the physical sensations of tension and discomfort in their bodies and release them by sinking their chi.  Sung means a complete release, a complete letting go of any sense of control, contraction, strength or binding inside your tissues and nerves, until holding of any kind is replaced by a complete sense of openness, space and comfort.

How the Author Learned to Sung
When I first started trying to grasp the term sung, I did not have an easy time. In my early days of training in Taiwan, a very friendly Chinese man who was not my main teacher helped me gain the sense of what sung meant. I knew minimal Chinese, he was the same with English, and our communications resorted to quite a bit of mime. My body was tense. He looked up the word sung in his dictionary and saw that it was translated as relax. He said in broken English, “You relax no good enough,” while mimicking how tensely I was trying to relax my body. I could not let go. Frustrated, he said, “Need sung. Have not enough sung.” He proceeded to demonstrate it  to me. Using vastly exaggerated motions, he let his joints go completely loose and stood before me with an obvious lack of any kind of physical tension.  I did not get it. He then demonstrated what he meant with two piles of coins. He put the first pile in a paper bag and laid a knife next to it. He said, “You want sung be like money. Make body be like money.” Then he took the knife and cut the bag. The coins poured out (letting go of physical tension), fell (releasing the chi downward), separated (loosening the insides of the body), scattered over the floor and soon stopped moving (the body fully sung.)

I tried again. He saw that I was just half getting it. So he made fists and raised his hands above his navel and suddenly, with his entire body loosening, opened his hands and let them fall to his sides. He grabbed the second pile of coins and brought them up to the same place above his navel and suddenly let go of them. They fell, separated and scattered on the floor. Then just as suddenly, he again let his body relax as his hands and arms visibly loosened and dropped to his sides just as the coins had to the floor. I put the two images together in my head and got it.

Next, my new friend asked me to touch his arm and belly. He stood with his hands at  his side. After checking that I was focusing, he relaxed and without moving an inch, released his body and went sung. I could feel his muscles turning to butter and a distinct wave moving down inside his body.