Permeability measures the ability of fluids to flow through rock (or other porous media).
A medium with a permeability of 1 darcy permits a flow of 1 cm3/s of a fluid with viscosity 1 cP (1 mPa·s) under a pressure gradient of 1 atm/cm acting across an area of 1 cm2.
Typical values of permeability range as high as 100,000 darcys for gravel, to less than 0.01 microdarcy for granite.
The odd combination of units comes from Darcy's original studies of water flow through columns of sand.
[1] Specifically in the hydrology domain, permeability of soil or rock may also be defined as the flux of water under hydrostatic pressure (≈ 0.1 bar/m) at a temperature of 20 °C.