@Grazing Dogs,
Lets take the solar system for example, Earth is moving around the sun, and the sun along with the rest of the solar system is moving through space as well, so it looks like the earth is moving in two directions at once... both around the sun and along with the solar system as a whole through space.
Look at it another way, lets say you tied a golf ball to a bowling ball with a string then catapulted the bowling ball through the air. The golf ball will probably spin around the bowling ball a couple of times while hurtling along in one direction with the bowling ball.... while orbiting around the sun, while traveling through space with the solar system, while traveling through space with the galaxy!
But space is a location, so no matter how complicated the movement may be, you only move in one direction relative to space.... i think?
And then i think i heard that space itself is also moving, by way of expanding!! that is the reason behind why some solar systems appear to be moving away from each other faster than the speed of light!