These are real proton collisions recorded by the ATLAS detector at CERN in 2015 and 2016. Each one kept here produced exactly two clean photons. Pair them up, compute the mass they came from, and plot it. Most pairs are random background. If a Higgs boson decayed into two photons, it leaves a small bump at 125 GeV. Add the data and watch.
Subtract the smooth background from the data. Random noise scatters around zero; a real particle leaves something standing at one mass.
A Higgs boson decays into two photons only about 0.2% of the time, and ordinary processes make photon pairs constantly. ATLAS and CMS announced the discovery in July 2012 after combining several decay channels to pass 5σ, the standard for "this is not a fluke". This page uses one decay channel of the public data and a simplified fit that counts only statistical uncertainty. Its significance is quoted only at the already-known mass, 125 GeV, because hunting across every mass for the biggest bump would find flukes.