In everyday life, only those items that are motionless on the the Earth's surface are considered stationary. In physics, the concept of "stationary" has always been relative to an observer. When Einstein spoke of relativity in 1905, it was to emphasize that measurements made by observers moving with respect to one another varied in more ways than had previously been realized. These new differences had gone undetected for hundreds of years because they are insignificant until the relative speeds involved reach a significant fraction of the speed of light.
Not only are the relativistic differences invisible in normal experience, but they also describe qualitative changes that most people find unnatural. The web link below contains several interactive pictures and animations designed to provide some visual understanding of the mathematics and consequences inherent in this unfamiliar model of our universe.