Sapphires have been prized for both their hardness and their color. On the Mohs scale (a ten point scale), where diamonds are a ten, corundum crystals are approximately a 9.

When you think of a sapphire, what color do you think of? Blue? Most people do, but not all sapphires are blue. Corundum crystals of gemstone quality in any color other than red are called sapphires, while the red ones are called rubies. The colors we see when we look at corundum crystals are all the result of impurities in the crystals. An intensely blue sapphire is the result of titanium and iron in the corundum crystal. A ruby is red due to the presence of chromium.
A clear corundum crystal contains a repeating unit of aluminum oxide and no other impurities (less than a few hundredths of one percent of titanium anyway). Therefore, if any corundum of color, besides red, is a sapphire, then would a clear gem be called a sapphire or something else?

Now, rubies and their color can be explained by crystal theory but sapphires and their colors cannot. Sapphire colors are the result of a process called charge transfer. Specifically, intervalence charge transfer or cooperative charge transfer, which is the transfer of one electron from a transition-metal ion to another.
Below is all of the science gobbly-gook to go along with this concept.
“Iron can take the form Fe2+ or Fe3+, while titanium generally takes the form Ti4+. If Fe2+ and Ti4+ ions are substituted for Al3+, localized areas of charge imbalance are created. When Fe2+ and Ti4+ ions occupy two adjacent sites in a corundum crystal, the transfer of an electron from the iron cation (positively charged) to the titanium cation (positively charged) can now change the valence state of both.
Fe2+ + Ti4+ -→ Fe3+ + Ti3+
This occurs because there is enough overlap between the outer orbitals of Fe2+ and Ti4+ to allow an electron to pass from one ion to another. This process requires energy.
Intervalence charge transfer is a process that produces a strong colored appearance at a low percentage of impurity. While at least 1% chromium must be present in corundum before the deep red ruby color is seen, sapphire blue is apparent with the presence of only 0.01% of titanium and iron. This energy jump is comparatively easy for electrons to achieve when light shines on the crystal. Charge-transfer transitions are strong because they are "allowed" by quantum considerations. The "forbidden" transitions in the ligand field-colored ruby are much weaker.
Sapphires undergo "heteronuclear" charge transfer as electrons are transferred between ions of different elements.
When the ions belong to the same element, homonuclear charge transfer occurs. A common example is the transformation that occurs in iron (Fe). The surrounding environments of the two iron ions have to be different.
FeA2+ + FeB3+ –→ FeA3+ + FeB2+ (electrons transferred from site A to site B)”
Random tid-bit:
A unique “orangy-pink” sapphire is labeled padparadscha, which means “lotus flower” in Sinhalese (the language spoken in Sri Lanka). Sri Lankans have a special affection for the color that’s traditionally been linked with their country.
Other uses for corundum crystals, besides being pretty:
Corundum crystals are manufactured for industrial or decorative purposes in large crystal boules (a boule is a single-crystal ingot produced by synthetic means). The crystals have been found useful for, and are created for, many industrial purposes. Synthetic sapphires are used in shatter-resistant windows, military body armor, scientific optical windows, and much more.
The scientific community prizes synthetic sapphires for their use in optical windows. They offer a wide optical transmission band from UV to near-infrared, are stronger than other optical materials or standard glass, highly resistant to scratching or abrasion, have an extremely high melt temperature (2030 degrees Celsius), are completely unaffected by all chemicals except some very hot caustics and fluorides, and they are the hardest natural substance next to diamonds.

The crystals are also made into sapphire wafers to be used as an insulating substrate in high-power, high-frequency CMOS integrated circuits. This type of circuit is referred to as an “SOS”, or “silicon on sapphire”, chip. The sapphire wafers are used because of their low conductivity for electricity and their high conductivity for heat. This means that the sapphires act as a good electrical insulator while helping to conduct heat away from the high-heat producing circuit.

Also due to the hardness of sapphires, they are used in the watch industry. Wristwatches can be found to have sapphire crystals and movement bearings in them.
OK, so there is a good bit of information for you to start with. You should have plenty of questions to go out into the world and continue learning more for yourself. Like what other interesting materials you might find inside common items like the watch you wear everyday?
What will I post about next? Probably not your wristwatch... but hopefully something else you'll find interesting!
References and Further Reading:
http://www.webexhibits.org/causesofcolor/index.html
Minerals: Their Constitution and Origin
By Hans-Rudolf Wenk, Andrei Bulakh
http://www.etymonline.com/index.php?term=sapphire
Gemstones: Properties, Identification and Use
By Arthur Thomas
www.Gia.edu
Sapphire: Material, Manufacturing, Applications
By E. R. Dobrovinskaëiìa, Leonid A. Lytvynov, V. V. Pishchik
http://www.gemresearch.ch/certs/report/auctrep2.htm