The mind and movement are reflections of each other. If you have a busy, racing mind, this is reflected in the way you move your way through your day and hold your posture. Fast moving mind is reflected in fast movement; striving mind is reflected in striving movement, etc. Nothing wrong with any of these states of mind, so long as it is what you would want to choose for yourself. It is when one of these states is an unconscious way of being that can result in being on edge, feeling anxious or not being able to enjoy stillness and calm.
So, if you want to calm your mind and thoughts you can do this through gentle, slow movement. By consciously bringing your attention to your movement you begin to bring yourself out of the mind and into your body and this already helps to create calm, but then by inviting yourself to move slowly you are actively encouraging your whole being to create a calmer state from the outside in.
Calming movement calms the mind, this is why it is easier to sit and meditate after moving through yoga flows and postures. If you've ever sat down to do a seated meditation practice without slowing your body down first you may notice it difficult to find your centre and focus. This may lead you to think that you can't sit and meditate or you just always have a racing mind when you come to sit and be still. See if a slow moving practice can help you find that state where you can sit and be still to notice your thoughts and your whole being.
This is why a dedicated practice of slow movement, such as yoga or Tai Chi, bring you into a calmer state of being which permeates your whole life. Your body and nervous system naturally slow down so you move with more grace throughout the day and your mind can be calmer when presented with any situation in life.
Change your movement to change your state of mind
As a simple exercise, next time you are walking somewhere, even just around your office or home, bring your attention to how you are walking. Is it brisk and hurried with a sense of needing to get somewhere? For busy people it becomes habit to move in this way, even when there is no real hurry. So can you consciously take slower steps? Would it make any difference to take the small extra space of time to get from A to B? Can you open up space in your day to consciously slow down? You don't have to move slowly, but just a little bit slower than before.
A guided variation of this exercise can be found under 'walking awareness' on my audio page.