"Here", in relation to what? Everything in the universe is in motion, except perhaps for the Microwave Background Radiation, a supposed remnant leftover from the Big Bang which (more or less) uniformly fills the universe.
With respect to it, we can actually detect the motion of our Milky Way galaxy, as one side of the MBR map is redshifted, the other blueshifted. Redshifts indicates we are moving away from that portion, while blueshifts indicates the opposite, moving towards.