The Earth itself is in motion (quite a considerable amount of it, in fact, on the order of hundreds of miles per hour as we rotate around the center of the galaxy) but you would never know it from intuition; we don't feel like we're moving, because we have no frame of reference.
A frame of reference is what makes motion and rest relative terms; being in motion, or being at rest, require you to compare yourself to another object. Since you can compare virtually any two things, motion and rest depend entirely on what is being compared, and whose perspective the comparison is viewed from.
We might assume that a complete absence of motion would be defined as rest; yet, this would require a universal standard of "zero motion", which does not exist. The universe itself is in motion, and thus, unless we can find some real or hypothetical nonmoving point, everything in the universe is, technically, in motion.