The new oven we bought about a year back is a convection oven - my first one. The advantages are:
• drier heat
• more even temperature in the oven
• shorter cooking time
I use convection for example for roasts. A roast chicken cooked with convection off will have some brown spots and some white spots. A roast chicken cooked with convection on will be perfectly evenly golden.
Sometimes perfectly evenly golden can be boring though. For that reason I like to use a combination of both baking and convection when roasting chicken. Meaning I just turn the convection on at the beginning, then turn it off, sometimes back on... depending on the way the chicken looks.
There are different types of convection oven. True convection implies a heating element around the fan, generating circulating hot air. Fake (?) convection (which is what my oven has) implies a fan that circulates the air that was already heated by the normal heating element at the bottom of the oven.