Hi, good question. There are sort of two answers. One, water itself is not visible to humans or fish, BUT we rarely find pure water in nature. Usually, water has other things suspended in it, like living things (bacteria, algae, etc.) or particles (silt, mud, etc.). These thing influence water clarity.

Water clarity is important because clear water allows sunlight to go further down into water, allowing for photosynthesis. It also influences predator-prey interactions and other behaviors. If water is very silty, it can even clog gills.

While water is not visible, it does bend light. This is called refraction. You can see this when you reach into an aquarium or any body of water. Your arm will not seem straight anymore. This site: refraction has some good images of how that works.

Can you think of other situations when seeing underwater is important? What sorts of things might cause your local water to be more or less clear?

Here are 74 answers to your question:

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I disagree with the answer that says our brains just remove the seeing-air signals. Air molecules are too small and too far apart for our eyes to see them. Water molecules in water are close together, but eyes can't see things as tiny as water molecules, which would all look the same and are all packed together.

Wikipedia has an article about fish vision, if you want to learn more: