A friend recently explained the stillness to me as sinking down into the ocean where it is quiet. There will always be activity (waves or thoughts) on the surface but it doesn't interfere with the sense of calm further down in the ocean. The deeper we are able to go down, the less the surface activity affects us. I had been feeling less than successful with my meditation, but this explanation helped me to be okay with the fact that I still have mindchatter and of late I've been able to distance myself (sink deeper) from it somewhat more. I hope this explanation might help someone else.
Love
Etoile