The computing needs of the LHC, especially when it comes to comparing various theories with experimental results, are enormous. Basically, the physicists' appetite for computing power expands to fill all available resources, because there are always more theories to test than there are computers to test them with.
Since budgets are constrained, especially in these economically difficult times, access to volunteer resources is seen by CERN as a great opportunity to expand computing capacity. We'll never replace the Grid's core function of managing the data mountains, but we could augment its computing power considerably. While the LHC World-Wide Computing grid is used at full capacity to handle the analysis of LHC data, there is need for additional capacity for simulations of LHC physics, ranging from theory to simulations of detectors as well as design improvements for future accelerators.
It's also clear to everyone in our community that getting the public more directly involved in LHC physics has great outreach benefits as well. So we see this as a win-win situation. And who knows, perhaps one day we'll be able to announce an important discovery that will have been made in part thanks to the volunteers. That would be cool!