What advantage do polarized sunglasses have over ordinary sunglasses?

The answer to that question is glaringly obvious. (That’s a little “light” humor.) Polarized sunglasses reduce glare!

Sunglasses have been around since Nero's time. Sunglasses would not become polarized, however, until 1936, when Edwin H. Land began experimenting with making lenses with his patented Polaroid filter. Polarized sunglasses lenses are invaluable in high-glare situations, such as driving, boating, golfing, surfing, and fishing. The polarized lenses help reduce glare, which can be a real problem in water sports and many other outdoor activities.  Choose polarized lenses if you are outside in high-glare situations a lot.

What is the difference between a polarized lens and one that is not polarized?

A polarized lens filters scattered and reflected light. For example, if you look at water with a standard lens, the surface of the water is reflecting light from all different directions so it's difficult to clearly see an object under water. Polarizing the light filters those reflected rays so you can see below the surface of the water.

               Without Polarized Lenses                               With Polarized Lenses