Chemical Formula: Al2O3
Color: Pretty much any color, but most commonly red, blue, pink, or purple.
Importance: Has one of two uses. High quality specimens are used in jewelry as gemstones. Red corundum is rubies and blue corundum is sapphire. Lower quality specimens are crushed to forma abrasives like sandpaper or files.
Other Interesting Information: Very easy to identify because it almost always forms in the shape of a hexagon. Is the second hardest mineral, behind only diamond.
My Take: Corundum is just one example of a mineral that everyone has seen, but no one knows the name of. Everyone knows rubies and sapphires, but no on ever knows that they come from corundum.
For More Information: http://www.minerals.net/mineral_glossary/abrasive.aspx