This is my favorite one:
What is this particle? We expect the Higgs boson to decay into two photons. The combined energy of the two photons is the same as the energy of the initial Higgs boson, because energy is conserved. This is the signal (S in the plot). We also expect other particle decays to produce two photons. This is the background (B in the plot). This happens very frequently at low energies, and less frequently at higher energies.
If we had just the background, we would expect a smooth decay, but what's going on at 125 GeV? Something is producing lots extra two-photon events! This must be because a new particle is being created at that energy! It produced two photons, so it must be a boson!
Technically, that's all we know so far about the new particle - it's new, it has a mass of about 125 GeV, and it's a boson - but it's very likely the Higgs boson that we've been looking for!
*As I explain in one of the following paragraphs, it's really the combined energy of the two photons but from conservation of energy we know that this must equal the mass of the particle that produced them.