A diving mask is a mask worn for being able to see under-water. It differs from swimming goggles in that it has a nose pocket built-in.
The nose pocket is vital because as you are scuba diving, the ambient pressure increases. Because your mask has air in it, if you don't equalise it, the pressure inside your mask will suck it to your face, which can cause discomfort, including pressure marks, bloodshot eyes etc.
The other reason you need the nose pocket is that you need to be able to pinch your nose shut, so you can blow against your pinched-shut nose. This helps you equalise other air spaces in your body; your ears and sinuses.
Clearing a dive mask - Because your nose is inside your mask, you can clear water that has leaked in from your mask: Simply look down with your head, apply pressure to the top of the map frame, and gradually tilt your head to the surface whilst exhaling through your nose. The air will stay in your mask whilst the water is forced out the bottom. Using this method, you can clear a fully flooded mask - it's even possible to take a diving mask off underwater, replace it, and clear it fully of water.
Fitting a dive mask - Masks come in many different sizes; the most important choice in finding the right mask is to buy one that fits well: you should be able to place it against your face (without the head strap), inhale gently through your nose, and feel it create a vacuum. You should be able to shake your head back and forth without the mask falling off. If it doesn't fall off, and feels comfortable against your face - congratulations, you've found the mask for you.