To look at nothing in particular, probably because you are tired of thinking or not paying attention. I studied so hard on my test that soon I began to gaze into space. Or: Hey, stop gazing into space and pay attention to your driving! If used in this way, it is an idiom. You are not looking into actual space (the atmosphere) but at nothing in particular--usually just straight ahead. But you can also use the phrase in a literal meaning, as in The astronomer gazed into space using a telescope.