What does this equation mean?

Energy deposition. A calorimeter is deliberately destructive. It stops the particle, converts its energy into a shower of secondaries, and measures a signal proportional to the total ionising track length in that shower. Because the shower is stochastic, the relative resolution scales as the inverse square root of the energy plus terms for readout noise and for imperfections that scale with energy: $\frac{\sigma_E}{E} \;=\; \frac{A}{\sqrt{E}} \;\oplus\; B \;\oplus\; C$. For the LHC general-purpose experiments the stochastic term is typically three to ten per cent for electromagnetic calorimeters and fifty to eighty per cent for hadronic ones, while constant terms sit at a few parts per thousand and a few per cent respectively [ 2 ] . The structure of that expression matters more than the numbers. At high energy the first term vanishes and the measurement is limited by the constant term, which is not a property of the shower at all but of mechanical construction, electronics stability and calibration. The instrument gets better with energy until it stops getting better, and what stops it is the experimenters’ knowledge of their own apparatus.