The "per MeV" refers to the fact that the flux rate $f(\theta,\phi,E)$ tells you the particle flux per unit solid angle *per unit energy*. That is, $f(\theta,\phi,E)\ d\Omega \ dE$ is the particle flux (in particles per unit area per second) within a small solid angle $d\Omega$ around $(\theta,\phi)$ and a small energy range $dE$ around $E$. If you want to find the particle flux per unit solid angle (without the energy part), then you need to integrate over all energies in some range, i.e. $$\hat f(\theta,\phi) = \int_{E_1}^{E_2} f(\theta,\phi,E)dE$$ which is the flux of particles per unit steradian with energy between $E_1$ and $E_2$. It's worth noting that when you have a histogram with energy bins $\Delta E_i$, then the quantity being plotted is $f(\theta,\phi,E_i)\Delta E_i$. To obtain $f(\theta,\phi,E)$ from a histogram, you divide the counts in each bin by the bin width. Conversely, if you have the so-called *differential flux* $f(\theta,\phi,E)$ and want to know how many counts to expect in a histogram bin at some energy, you simply multiply it by the bin width.