Faster cooking: Since hot air is blowing directly onto food instead of just surrounding it, food cooks about 25% faster in a convection oven.
Even cooking: Regular ovens can have hot spots, depending on where the heating element is, but the fan in a convection oven will circulate the air to help even out the temperature variances.
Better browning: Air in a regular oven can become a bit humid since moisture can't escape, steaming food instead of roasting. Convection creates a dry atmosphere that caramelizes the sugars faster when roasting, so foods like meats and vegetables get browner, but the interiors stay moist.
Saves energy: Since food cooks faster in a convection oven, and generally at a lower temperature, it's a bit more energy efficient than a regular oven.