During each session of meditation, after energy centres have been activated (hopefully) from the Muladhara chakra (base of the spine) upwards, the trunk tends to sway at Muladhara and then there is a feeling of some energy rising. At Visudhha chakra (throat) there is a definite swaying around the neck settling down at spiritual eye. My question is, generally, what does the upward movement mean and specifically, what does the fairly vigorous swaying of the neck mean?
—Syamal Mitra, India
What you are experiencing in meditation is fairly common and is an indication that the kundalini energy is awakening and moving upward (a good thing!) in your astral (energetic) body. The movement of inner energy is what causes your body to sway, including the swaying of your neck.
Working with the kundalini power can be a little tricky, and it would be best for you to have some specific guidance for how you do it—to keep you safe and on the right track. My best suggestion would be to work with an Ananda Sangha teacher if you have one near you, or to study this topic in The Art and Science of Raja Yoga, which is a Part 2 of Ananda Sangha Worldwide’s Kriya Preparation Course.
But for some brief bits of advice for now, whenever this happens to you in your meditation, pause and say a sincere prayer for help and guidance from God and gurus. Then try to internalize your energy consciously to bring your awareness more into the inner (astral) spine rather than the outer (physical) spine.
Eventually the rising of kundalini can be brought under your complete control and aid you greatly in your spiritual journey.
Keeping your gaze and attention at your spiritual eye and keeping your heart open in a devotional way will also help you very much in this process of spiritual awakening.
If the “vigorous” swaying of your body or neck feels like it’s becoming too much, then open your eyes for a moment, say a quick prayer for help (it will come!), and then re-center yourself in devotion at the heart chakra for a while.