Stillness is a calm, quiet, motionless state. As you look out at the lake, the stillness of the water is a sign that you should take out the canoe rather than the sailboat.
When there's stillness, you can hear very few sounds and see very little movement. The stillness of a quiet mountain cabin may be just the escape you need from the busy, noisy city — although you may find that stillness to be a little spooky at night. You can also use this word for a more specific example of motionlessness: "The butterfly's stillness allowed me to get a good look at its beautiful wings."