The Mystic can enchant items, improving or modifying their stats in some unknown fashion. The Diablo 3 team hasn't given any specifics about what enchanting actually does, but they've said that players will probably want to enchant every item they can, so it's evidently a highly desirable bonus.
The first mention of "enchanting" came from the Caravan FAQ, released in August 2010 at the Gamescom expo. There was just a single line about the Mystic, which credited her with Enchanting, but didn't give any indication what that meant.
A quote from an interview with indiablo.de from Gamescom 2010 confirms that the bonuses are not random:
More information on Enchanting was revealed by Jay Wilson in an interview at Blizzcon 2010. 
From the way Jay describes "finding enchantments" it makes them sound like recipes. Recipes are what the Artisans use to craft new, semi-random items in Diablo III's form of gambling. Artisans know some recipes to start with, and acquire more through their level up training. But the best recipes in the game are found as drops from monsters. These recipe scrolls are then given to the appropriate Artisan, and from then on that Artisan can craft that item.
So will the Mystic know some enchantments to start with, and learn others from found enchantment scrolls?