I am having trouble finding information on a definition in P. Hanham's PhD thesis paper. recall that given a discrete group $G$ a $G$-CW-complex $X$ is a CW-complex equipped with a topological $G$ action such that if $G$ acts on a cell in $X$ trivially, then $G$ acts on each point in said cell trivially. Hanham says a *free* $G$-CW-complex ($G$-CW-complex with trivial stabilizers) is said to be *a model for* $EG$ if $X/G$ is a $K(G,1)$ Eilenberg-Maclane space.

My question is, why $EG$? Is this just a definition or is there more that i can learn about this '$EG$'. Hanham says nothing more on the topic. I'm pretty sure there is something more to this but i am having difficulty finding this online. If someone could point me in the right direction, I would greatly appreciate it. Thanks in advance!