The short answer is: there is no application... for now. As @theabsolute said it, this concerns fundamental research: we are trying to understand how the universe works, and this has no direct application. However, the theories that are being developed may play a crucial role in the future. I like the GPS example. In 1917, general relativity was a theoretical curiosity. Today, 100 years later, it is a well established theory that allows, for instance, GPS to work as expected.

This being said, one should not underestimate the outcome of fundamental research: we are trying dozens of students to solve complicated problems during 3-6 years (the usual timescale of a PhD thesis). This skill is well demanded in the private sector. In addition, we are building un-patented technologies for our experiments, so that everyone on Earth can use them for free (imagine a world where everyone will have to pay one cent to CERN for every click on the Internet ;) ). And so on.