Guillermo wrote this explanation for you, which might help.
You can think of the selection of species s for temperature T as a *preference* of s for T. Its calculation uses as input the maps of potential distribution generated by the Maxent scheme described before. It may also use maps of *actual* distribution, if one had them.
We interpret the maps as a stochastic variable, M_i(s), distributed over space, where i runs over the map identifying each site. For each value of T, there is a subset of sites of the map that have that T. Some of them have a large M, some others have a small M, etc. 【We can build the *probability distribution function* (PDF) of this variable that will characterize such distribution of values of M. For this, you run over the map searching for the T-temperature sites, and count how many of those sites have the value M(s).】*** You don't use an exact value of M, but instead define a "bin" (a small interval in M) and count how many sites fall in each interval. ***

This gives an approximation of the exact mathematical PDF, in the form of a histogram. You can play with the bin size to balance between smoothness and loss of features in the resulting histograms. There should be a large range of bin sizes where the histograms have the same shape (width and number of peaks, for example). The resulting distributions (histograms) should be normalized to be interpreted as proper probability distributions. These are the distributions shown in Fig. 5.

Once normalized, their meaning is the following: given a temperature, and an interval of selections, say (M1,M2), the area under the curve is the probability that species s "selects" ("prefers") ANY site with selection between M1 and M2. If the animals should have absolutely preferred a certain temperature, say T0, and nothing else, then the histogram for T0 should be a sharp peak at M = 100%. Any other histogram, built in the same way for any T not T0, should be a peak at M = 0%. But since animals are not so narrow minded, and there are other variables at play, the histograms are more extended in M, and with shifting shape as you change T. This is the core idea.
As you can imagine, you can do the same with any other parameter, not only the BIO5 or BIO11 temperatures that we used. It can be landcover, precipitation, height, whatever.
The distributions of selection (or preference, I would rather have called them preference) contain all the information we need to discriminate between species (Fig. 5, showing just two temperatures). 

But, as continuous functions with a complicated shape, that change from temperature to temperature, their interpretation is not direct. For this reason we chose to define a single index derived form them. This is the parameter R(T), defined buy summing M over the sites that have a certain temperature T. Observe that R(T) is a function of T, not of M as were the PDFs above (Fig. 5). If the distribution had been single peaked gaussian-like functions, we could have used the mean. But our distributions were multi-modal, and we devised this method, with the result shown in Fig. 6: R(T) allows to distinguish between species, as shown in Fig. 6B. Figure 6A is the same, but more visually appealing: the radius of the balls is the height of the curves shown in Fig. 6B.
I hope that this explanation has made the procedure clearer. The language in the paper is sometimes a little too terse.