Concentration to mass relation describes how a parameter of a dark matter density profile changes with the mass of the halo.
Usually the concentration parameter (denoted $c_{vir}$, $c_{200}$, etc) implies the ratio of the halo radius ($r_{vir}$ or $r_{200}$) to the characteristic radius ($r_s$) of the Navarro-Frenk-White density distribution. Both observations (See e.g. a ScienceWISE collection of bookmarked paper here) and numerical simulations of structure formation show that the more massive halos are less concentrated.
In the Lambda CDM concentration to mass relation follows a power law trend: where the index $a \approx 0.11$ (see e.g. [2]). In warm or mixed (cold plus warm) dark matter models numerical simulations show that the relation between concentration and mass flattens at low mass end (even for halo masses above free streaming scale) (see e.g. [5] and [6])
The concentration-to-mass relation depends non-trivially on the redshift (see e.g. Bullock et al. [1] (2001), Maccio et al. (2008) [2]) and cosmological parameters [2, 7].