Why does Earth seem to be standing still?
There are two factors in why the Earth may appear to us to be standing still: constant speed and perspective.
The truth is that our planet moves very quickly throughout space, about 67,000 miles per hour around the Sun. On top of that, Earth is spinning at about 1,000 miles per hour. So how don't we get dizzy or fall over if our planet is moving so fast? Lucky for us, Earth's speed in orbit and rotation are constant. When Earth moves, gravity has everything fixed in place to move with Earth. If our planet's gravitational pull were not so strong, we might well be left behind and see just how fast Earth really moves. If Earth's speed were to somehow be changed, we might very well notice it if the change was significant enough.
Perspective is the second factor to consider in why we don't feel or notice much of Earth's motion. From our relatively fixed and stable points on the surface, we can observe changes in Earth's position over time. Have you ever noticed how the stars of the night sky are different throughout the year? This is a result of our revolution and rotation as a planet. These stars and planets are so far away, though, that we may as well consider them to be fixed points in the distance. Throughout the year, we are essentially "passing them by." Think of how quickly objects seem to pass by when you're riding in the car or on a bus--objects far away seem to pass more slowly, while those close up pass by quickly. It's all to do with perspective. If we had some celestial bodies at fixed points much closer to us, we might be able to look into the sky and sense just how fast Earth really is moving.