In yoga, stillness is as much a state of mind as a lack of movement. Most of us don't spend much time thinking about the material nature of human consciousness, but in classical yoga, consciousness is at the heart of the practice.
According to Patanjali's Yoga Sutra, the so-called contents of our consciousness—perceptions, thoughts, emotions, memories, fantasies, even dreams—have a kind of material existence (though, of course, the matter is a lot subtler than that of a tree or a rock). Furthermore, these contents are in constant fluctuation. The word Patanjali uses in sutra I.2 to aptly describe this movement is vritti (pronounced VRIT-tee), which means "to revolve" or "to whirl about."
While we can't physically touch the vrittis, or fluctuations of mind, we can easily experience them. Close your eyes and, for a few minutes, direct your awareness away from the outer world. If you're a contemplative person, you've probably done this many times before. It's possible to consciously step away from the contents of your mind and observe them more or less "objectively," at least briefly.