All the stars in our galaxy are moving relative to one another, usually at speeds no more than about 100 kilometers per second. Some stars move much faster, and a few have huge velocities, of the order of 1000 kilometers per second.
These hypervelocity stars have an interesting history. Astronomers believe these stars probably started life as one half of a binary system with one star then being captured by the powerful gravitational field of the supermassive black hole at the center of our galaxy with the other being flung away like a sling shot.