A local system on a topological space is a locally constant sheaf. A finite-rank local system of vector spaces on a connected locally path-connected and locally simply connected space is equivalently a representation of its fundamental group, after choosing a base point. Transport around loops gives the representation, called monodromy. On a simply connected space, such a local system is constant.
In the étale setting, a lisse 
-adic sheaf is the analogous locally
constant object, described by a continuous representation of the étale
fundamental group. The geometric
Langlands correspondence uses local systems for the Langlands
dual group as spectral parameters.
