A Chern-Simons gerbe is a lifting gerbe for the shifted central extension
given by the string group.
This is called “Chern-Simons gerbe” because for a given $G$-principal bundle $P$; the corresponding Chern-Simons gerbe has the property that
the integral class of the gerbe is the first (fractional) Pontryagin class of $P$
a connection on the Chern-Simons gerbe has as curvature 3-form the Chern-Simons form of a connection on $P$.