[Nizzle (OP)]

The Higgs Boson has been theorized, and soon (hopefully) we'll prove it's existence with the LHC experiments.
But what's next?

What can the theoretical physicists prove by proving the existence of the Higgs Boson?

[DoctorBeaver]

It won't just be what the discovery of the Higgs boson will prove, but also what it will disprove.

If (and it's a big IF) the Higgs boson is discovered it would point to the Standard Model being correct. Models that do not incorporate the Standard Model would therefore be shown to be false. There are any number of theories/hypotheses around that are alternatives to the Standard Model. Physicists working in those areas would need to switch their research to theories/hypotheses that incorporate the Standard Model. Research efforts would be more focused in directions that will have been shown to be valid.