The radial distribution function (or RDF) is an example of a pair correlation function, which describes how, on average, the atoms in a system are radially packed around each other.
The shape of the RDF can tell us a lot about the system we are studying. Firstly, at short separations (small r) the RDF is zero. This indicates the effective width of the atoms, since they cannot approach any more closely. Secondly, a number of obvious peaks appear, which indicate that the atoms pack around each other in `shells' of neighbours. The occurrence of peaks at long range indicates a high degree of ordering. Usually, at high temperature the peaks are broad, indicating strong thermal motion, while at low temperature they are sharp because the thermal motion is much less. They are particularly sharp in crystalline materials, where atoms are strongly confined in their positions. At very long range the RDF tends to a value of 1, which happens because the RDF describes the average density at this range.