I'm not sure if you mean "air" or "too much air", but although I'm not a chemist, I'll try to answer both using a laymen's explanation.
Air is always in the water naturally from molecular gas diffusion. (The amount is spread around the water and is in such a small amount that it's not obvious to the naked eye.)
Fish breathe air, not water, and they get their air in the water by way of their gills. (Some fish breathe from the source and just go to the surface and grab a mouthful of air instead.) But either way, that's why if you cover the surface of the water in a fish tank with a sheet of plastic (or oil), the fish will suffocate. (Plastic = no diffusion = no more oxygen.)
What's bad is when you have too much gas in the water and it's in the form of compressed air or micro bubbles.
The most common culprit is not air bubble diffusors or HOB water flow or most filters, since they create pretty large bubbles, but instead compression of the air (gas) in the water (which can easily happen in pipes as cold water comes to your house under pressure.) This creates a super saturation of gas. As already mentioned, you can have the problem if you see a somewhat milky, cloudy effect when you take a glass of water from the tap that clears up within a short period time.