Item rarity refers to how rare the game system considers a dropped item. This does not necessarily mean that the item is extraordinarily rare to find, especially from other players.
Different items in the game have a colored name. This coloring system gives you an idea of the likelihood that you will get the item if you are farming specifically for it. It is often easier to purchase a "rare" item from the Auction House rather than spend hours trying to obtain the drop on your own.
Cash Shop items always have a bright pink name.