As has been said, red wine glasses are generally wider because increased exposure to air helps the deeper and generally more complex flavors of red wine develop fully. Larger surface area means higher air exposure, and the wider bowl of red wine glasses allows for more wine to be exposed at any given time.
In general, white wines do not require as much oxidation for the flavors to expand, thus partly explaining the narrower shape. However, there are other reasons. Heat transfer is another big reason for the more narrow shape of most white wine glasses. Larger surface area means higher oxidation, but it also means that more heat will be transferred into the wine from the surrounding air. The larger the surface area of a cooling/warming object, the higher the rate of heat transfer, so having a narrower opening decreases the exposed surface area, ultimately keeping the wine chilled longer.
One of the biggest reasons, however, is flavor distribution. Different kinds of glasses are made to deliver different sorts of flavors to the optimal part of your tasting apparatus. Generally, red wines tend to feature flavors that are best tasted with the tip of the tongue and the front of the mouth, while white wines are usually comprised of lighter flavors that can be more thoroughly processed by the back of the mouth. The wider bowl of the red wine glass and narrower shape of the white wine glass both cater to this trend, respectively.
For more information on different types of wine glasses (including a break down of some of the different types of red wine glasses), take a quick look at this article. It details all of the different types of glasses, as well as which type of wines they are designed to optimize.