The temperature variation in the CMB corresponds extremely precisely to what is expected if the CMB is isotropic (the same in all directions) in some frame and we are moving with respect to that frame. If you've seen the usual pictures of CMB temperature variations, the "dipole" temperature variation due to our motion (example) is about 10 times more extreme than those temperature variations, and those nice pictures are only obtained after subtracting it off.

Put another way, we can say purely by analyzing the CMB that there is a reference frame in which it is about the same in all directions, and we are moving at 370 km/s with respect to that frame.