I expect that it will help gain a deeper understanding of physics which in turn will enable the development of new technologies. These new technologies could in turn help us greatly in facing our biggest challenges.
It's not a direct result of CERN, but a byproduct. They have special requirements for cooling, data processing, engineering, etc. It helps to push for improvements in these fields.
After all, there was a plethora of internet services early on, the web just happened to eat most of them.
Perhaps I'm undervaluing the merits of taking a shower to solve a problem unrelated to cleaning my body, metaphorically speaking.