Delocalised electron in graphite
It's just a matter of definition. If a "layer" is understood as an infinitely thin plane passing through the centers of carbon atoms, then the electron density of the huge delocalized $\pi$ orbital is located above and below that plane, i.e., technically between layers. If a layer is defined so as to include whole atoms, then the said orbital is within layer.

In any case, the delocalized electrons are more or less "free" to move along the planes and not perpendicular to them, which explains the high anisotropy in electrical conductance and other properties of graphite.