There are several ideas about how it works. In short: it promotes blood flow, relaxation of muscles and healing. My understanding is that the insertion of fine needles provokes an immune system response that improves blood flow. I have personally observed magnified ultrasound showing tiny rivulets of fluid moving in response to acupuncture needling. It might enable the muscles to slide more easily in relation to each other. This would explain the idea of fascial release. MRI scanning has also shown a response in the brain where needling has interrupted some nerves conducting pain signals back to the brain. We might conclude that acupuncture might calm the nerves and improve blood flow.
Initial responses vary from a dull ache, a bubbling feeling under the skin, sweating in the skin to a deep response in an organ. For instance when I inserted a needle at Liver 3 in the foot a lady said: Oh, I can feel that in my liver!
Traditional Chineses Medicine, TCM describes many acupuncture points in the skin that stimulate the flow of qi or life force. In the West the word meridians, has been used to describe Chinese terms for channels of energy.
Muscles and organs are covered in elastic tissue called fascia. It allows the muscles to slide over each other and links the movements of your limbs. The fascia co-ordinates the movements of your limbs.