I can't say I totally get it (as a non-physicist), but I always had the impression it was important because without it we don't know how any atom gets its mass, and therefore is important for working out how gravity works and how atoms hold together. I figure if we can sort that out, Star Trek type space travel might become a reality (eventually). Physics and engineering in general have already given us touch screens, voice activated computers, scanning equipment akin to tricorders and some degree of teleportation so I figure warp drive will happen eventually.
CERN itself has made so many advances to make the collider and associated science possible that I don't begrudge them the money, which probably works out at about the same as the royal family costs per person. It also brings together thousands of people from ~110 countries for an entirely peaceful purpose, which I also think is a good thing.