Let's consider $X$ a (locally connected) topological space and $\mathcal{Sh}(X)$ the topos of sheaves over $X$. If you see sheaves as étale spaces, locally constants sheaves correspond to covering spaces.

**Is there an internal (topos-theoretic) characterization of the locally constant sheaves?**

I've searched in *Sheaves in Geometry and Logic*, but I haven't found anything, and in the nLab there seems to be something but I do not understand it (and it does not really look like an internal characterization).

meansyou have $mathcal{E}$togetherwith a geometric morphism $mathcal{E} \to \mathcal{S}$, so even for based topoi, this definition is internal. Anyhow, this level of generality is not needed to answer the question. Every topos can be regarded as a topos over $SET$ in a unique way, since $SET$ is the terminal topos, as Mike points out. – David Carchedi Mar 14 '12 at 11:43