A convection oven or fan assisted oven is just like a standard oven, except that it uses a fan to drive heat rapidly from the heat source to the food, resulting faster cooking at a lower temperature.
In a conventional oven, the main heat source is at the bottom, and when you bake, natural convection draws the heated air up past the food to the top. However, airflow patterns in standard ovens are erratic and unpredictable, and they are affected by the food in the oven: if there's not much food, or if it's very thin and spread out (think cookies on a cookie sheet), the heat is transferred more efficiently to the bottom of the food than the top, resulting in burnt bottoms; whereas if the oven is too full, the heat won't circulate properly, and the food won't cook well. But the fan in a convection oven sends the hot air flowing evenly into the food from all sides, ensuring that it cooks speedily and evenly.
In general, you can reduce cooking temperatures by 25 to 30%, and cooking times by 20%, when using a convection oven.
I have read some conflicting stories about the advantages and disadvantages of convection ovens.
For example, in discussing how to roast turkey in a convection oven, one website notes that the air circulation causes greater moisture loss in turkeys than in conventional roasting, with a corresponding 3 to 5% lower yield of meat. (Lowering the temperature should help to combat moisture loss.) This website also advises against crowding large items like turkeys in the convection oven, because this inhibits air circulation and slows cooking.
On the other hand, another site comments that convection baking reduces shrinkage and can result in an extra serving in some (admittedly unspecified) foods; and that items in pans can be placed very close together in a convection oven, thus allowing more items at a time to be cooked than in a conventional oven.
I don't have enough experience with a convection oven to adjudicate between these claims, but everyone's pretty clear that convection ovens are versatile and do a good job at cooking, warming, roasting, and baking anything that can be cooked in a conventional oven. In fact, one website comments that if it weren't for the space sacrificed to the fan, convection ovens would be the standard for ovens.