R-module

A module $M$ over a ring $R$ is an abelian group with a ring homomorphism

of $R$ into the ring of endomorphisms.

It can be thought like if you have an "action" of the ring $R$ on $M$, similar to what happen with group actions: a group homomorphism $G\to Aut(M)$.

Consequently, given an abelian group $M$, it is trivially an $End(M)$-module, and given any subring $S\subset End(M)$ we have an $S$-module structure in $M$.

Important case: simple module.