Dyes
Dyes are a new feature in Diablo 3 that Jay Wilson revealed during an interview [1] after the GamesCom 2010 Artisan Reveal. It allows the player to color their armor in different color, there are around 15 different colors the player can use.
System
Bashiok has revealed [2] some specifics about armor dyeing. There are specific slots where you can dye your armor, usually these slots are areas which have something to dye, for example a sword might not be dyeable. An item cannot be dyed fully, as each item is hand-crafted by the Developers to have dyeable areas, such as a piece of cloth hanging down a chest item or an entire robe. Bashiok was careless to drop the word slots, which implies plural, which might indicate that items may have 1 or more areas that can be dyed.