Some people study Number Theory. Others study the Geometry of Manifolds. In TCS, we study the Power of Computation. We prove theorems, just like in any other pure science. What can be computed, how well, how fast, with what techniques, and what are the limitations? In the same way that number theorists were long fixated on Fermat's conjecture, our eyes are fixed on the distant P versus NP problem. Instances of applied problems are a chance for us to test our understanding of the hidden structure. "Reality check" means an example against which to confront our ideas on computation. Whenever a problem is hard in theory but easy in practice, or vice-versa, it's an invitation to revisit our assumptions and refine our models.
The real world is useful, as a tool towards developing a better theory.