A convection oven is one which has a mechanism to maintain a very even temperature. There is a fan to eliminate hot and cold spots. The result is that it bakes very evenly. Sometimes a little faster although that wasn't the reason I wanted one.
Baked goods benefit most. You get a very consistent result, lots of even browning, its hard to burn things (although God knows possible). My breads are rising better and more reliably, cakes even, pies golden and souffles....well, as I said I took a picture, maybe for my Christmas card!
I'd heard about them for years. I believe a lot of professional chefs use them. I am not sure they are much use unless you bake. I also make my main dish casseroles in it, too and they come out lovely.
No, I don't work for GE or an appliance manufacturer....just a nutty American nurse in love with an appliance.