The Blue Hole is blue because clear water is blue. Water absorbs the red part of the visible light spectrum but scatters or reflects the blue part of the spectrum, and this is the color you see.
This is why a swimming pool looks blue, even if the tile or liner is white. You need a 6-8 foot column of water to see the blue color clearly. Water in a bathtub is just not deep enough to see the blue color.
This pool, amazingly, is 30 to 40 feet deep (we threw a rock in and watched it settle to the bottom). The water is so clear that the depth is not apparent, but the blue color is very strong.
If you want a more technical explanation, go here.
