Moving meditation and seated meditation have different objectives, though both are called meditation. In this post, I'll focus on moving meditation.

When we start moving meditation (e.g., taijiquan practice), we start at a physical level, and once the logistics of the physical movements are sufficiently internalized, the focus goes inward, from external form to internal feeling. This is when we start feeling our life energy (qi), internal organs, the flow of blood, etc. After a period of diligent practice, we notice that the feeling of qi is not scattered anymore, but is becoming more focused, and we develop a deeper sensitivity to the ebbs and flow of qi within our system.

Along with sensitivity, many mental patterns become observable. We start entering into a witness consciousness state, wherein during the practice, various mental activities and proclivities start to become apparent. With proper guidance from a good teacher, we can understand our own minds at a very deep and profound level, delving not just at the surface, but diving into the depths. 

With time, understanding, and patience, the mind becomes calm and still during the practice. But the witness state expands into the rest of our day. Gradually every action, every thought is observed as if by a neutral witness. Little by little, the stillness and calmness of the mind during practice time spills into 'normal' time. Little by little, every moment becomes the present moment. That is when we enter 'meditation' in movement.