The plot here is showing events with two photons, with the invariant mass $m_{\gamma\gamma}$ of the two photons plotted. The invariant mass is given by $m_{\gamma\gamma}=\sqrt{(E_1+E_2)^2-(\vec p_1+\vec p_2)^2}$. This particular quantity is of interest because if the two photons came from a decay $\rm X\to\gamma\gamma$, then by conservation of four-momentum, $m_{X}=m_{\gamma\gamma}$.
On the top plot, the lower red line is what we expect to see from Standard Model background events. That is to say, basically everything except $\rm H\to\gamma\gamma$. The lower plot shows the same data, but with these background events removed, so it shows only the Higgs peak and some statistical noise.
These peaks show that we have more events with two photons with a specific invariant mass than we would expect without the Higgs boson. In other words, they can be interpreted as a measurement of $\rm H\to\gamma\gamma$.
The Feynman diagram you show is one contributor to the result above. The $W$ boson can be replaced with any charged Standard Model particle and that will also contribute. But the Higgs boson couples more strongly to more massive particles, so the primary contributing diagrams are the one you show and a similar one with the W boson replaced by a top quark. The next heaviest charged particle in the Standard Model (the bottom quark) is much lighter and so doesn't contribute that much.
