By contributing enormously to our understanding of quantum physics. If you use a computer or consume electricity, this just might be important.
Because it will create a whole new universe of stuff. Lots and lots of stuff. If it is a bad universe full of bad stuff we can ship the liberal/progressive hippies off to it.
Well shoot, the first one benefited us, no? :-)
It could allow physicists to discover the Higgs boson. The Higgs field is (assuming the current standard model is correct, which it may not be) what imparts mass to particles (some particles, such as photons, seem to not interact with the Higgs field, which is why they appear to have zero rest mass).
There are an almost endless number of advances that could result. Two examples are:
If we can control mass via the Higgs field, we could use it to evoke gravitational containment of hydrogen, giving us an easy path to fusion power. With the containment problem solved, the world's energy problems would be a thing of the past.
If we can control mass via the Higgs field, we could use it to eliminate the effective mass of a vehicle, giving us a sort of "antigravity". This would make a variety of activities, such as space launches, almost trivial.