Slate is an unremarkable metamorphic stone. It should not be confused with slade, an entirely different (and quite spoileriffic) material.
"Slate" is the name of the second month of the Dwarven calendar, covering mid-spring.
 In Real Life
Slate is shale which has been metamorphosed at high temperatures and pressure. It is a common form of roofing where it can be accessed easily.
Slate can range in color from a very dark, slightly blue grey to a light pink, and splits along layers, which are perpendicular to the pressure the slate was metamorphosed in.