Another patently ignorant meme.
When you're in a moving vehicle, it is not moving relative to you. It "feels" stationary. You don't feel like you're moving relative to the vehicle because you aren't, yet when you look outside you realize you are moving, and will normally feel the de/acceleration associated with that movement.
Similarly, on a moving planet, you don't notice the movement normally, because you're moving consistently with the planet. It's not changing velocity so you don't notice its movement, but you may observe the fact of movement by noting the changing position of the sun, moon, and stars relative to your location.