This is the diphoton channel, so it looks at the cases where the Higgs decays into two photons. There are also other collision processes (I don't know which) that result in two photons. This is called the background and you can not tell from the photons what process produced them.
The plot is a histogram. For every photon pair you find, you determine their combined energy, that is on the horizontal axis. Then you count the events with an energy between 120 and 121 GeV, and you plot that number of events on the vertical axis at m=120.5GeV, giving you the events per 1 GeV.
The Higgs particle is most likely to be produced when the available energy is close to its rest mass, so you expect an excess of events around a certain energy, on top of the background.
They fitted a combination of a polynomial and a small peak to the data and this is the result. Of the total of around 66000 diphoton events in this graph they attribute around 300 to the Higgs.
This peak doesn't seem to be much, but it was there already in the 2011 data and it grew when combined with the 2012 data. It is also present in another channel, with the Higgs decaying into other particles. And it has been found by both experiments. The conclusion is that the signal from the Higgs is real, it has been found.