Grey Cast Iron has a very high carbon content (4-7%), which when cooled slowly precipitates out of solution with the iron and forms little flat flakes of graphite between the iron crystals. This creates it's many properties.
It's brittle because every graphite flake is not just a very easy path for cracks to split apart the iron crystals, but a place for such cracks to get started.
It has low tensile strength as the graphite flakes don't "stick" the iron crystals together well, making the whole structure fairly easy to pull apart.
It machines well because every graphite flake is a place for the chips to break - that's why you get that fine "dust" for chips, and the graphite provides lubrication for the cutting tool.
It doesn't transport vibrations well because the graphite flakes, not sticking well to the iron crystals, provides an energy absorption barrier to the vibration. It can't take large amplitude vibrations (like from a hammer blow) because they will cause cracks, but small amplitude vibrations from a motor running or cutting tool do get absorbed.
If given a simple heat-treatment (i.e. induction or flame-hardened, basically heated and held at temp long enough for the carbon to dissolve into the iron, then cooled quickly to prevent it from precipitating out again) it will become extremely hard due to the very high carbon content.
The graphite flakes do pierce the surface and provide a surface lubrication as well, so it slides easily on most other materials without a lot of wear occurring to either surface.
If given a complex heat-treatment and a very small amount of alloy material (0.10% magnesium) you can transform the graphite flakes into spherical carbon nodules, turning it into a material with much higher tensile strength referred to as Ductile Iron, Nodular Iron etc depending on trademarks. Yes, the material the auto industry calls nodular iron used in crankshafts is the exact same stuff machinists call ductile iron used in vises.