The simplest way of answering this question is to say "Try opening your eyes underwater and you'll know why you need a mask", but there is a difference between knowing and understanding. Those of you who have tried already, know that everything is blurry. You could be in the clearest of water and everything would still be blurry. In order to understand this phenomena we must first agree that we need light in order to see.
Originally light was thought to travel in rays but later studies revealed that it moves in waves. These waves are electro magnetic and though the spectrum of light waves is broad, we only use part of that spectrum with respect to vision. This is called visible light. They are affected by the various mediums through which they travel. The denser the media, more dramatic the effect. The rays from space have to pass through the atmosphere of our world and when it hits the air environment the velocity decreases. For snorkelers, they then have to pass through water, glass and the air space inside of the mask. Water is denser than air and the glass of the mask is denser than both air and water. This means the velocity or speed changes three times as it passes through those media. In addition to losing velocity the light rays actually bend at the boundary between media. This bending is called refraction.
Our eyes are perfectly suited to this air environment. The irises dilate and contract to control the intensity of the light while our corneas and lenses help to bend the rays at just the right angle for our retinas to (at the back of the eye) to turn them into electronic signals which they send to the brain to interpret. They are limited as to how much they can actually bend the waves back to a position that puts the image on the retina. If they are out of position then the eyes will not focus and everything looks blurry.
Wearing a snorkeling mask puts our eyes back into an air environment putting two media in between the water and the eyes. The light rays will bend at the boundary between the water and the lens of the mask and again at the boundary between the lens and the air space. This is usually is enough bending to get them properly positioned on the retina for the eyes to be able to focus again.
One other point should also be made about refraction from an air to water environment. This being that the water that we snorkel in is constantly moving. Because of this the light waves can be bending in several different directions at the same time. This can also inhibit the eyes ability to focus.
If you are a person that wears glasses on land, you can still go snorkeling. There are a few manufacturers such as Deep See that make diopters that will replace existing lenses and there are a couple of places that will grind out lenses to your own personal prescription which are chemically bonded to existing lenses. And there is always contacts.
So know you can impress your friends with this knowledge when they ask you about vision under water or simply tell them to put their head under water and see for themselves.