To outrun someone is to move faster than they do. Your lazy cat might enjoy hunting for mice, although the mice always seem to outrun him in the end.
You can outrun an opponent in a race, and you can also watch a video game character outrun a pursuing zombie — outrun can also mean "escape from." Your dog might enjoy chasing cars, never managing to outrun them. More figuratively, you can say that your hopes always outrun the reality of a situation. In other words, what you dream of exceeds what actually happens.