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The likelihood of a specific item to be chosen to spawn, out of a group of equally valid choices.

For example: The game decides that a Unique Ring should drop.
There are many possible outputs. Nagelring's higher rarity (283 in cLoD) as compared to, for example, Raven Frost (188.7), makes it the likelier of the two to drop.

Rarity is expressed as items per 1000 items of that type, e.g. The Stone of Jordan is listed at 18.9/1000. This means that out of 1000 unique rings dropped that were high enough level to be The Stone of Jordan, 18.9 would be, on average.

Rare means that it is something you don't find often, and most of the time you don't. You have a better chance of rare's dropping on higher difficulties, and on higher monsters, specifically bosses

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