Air looks invisible because it sends very little color to our eyes. Most objects seem to have color because they absorb some light wavelengths, or colors, and reflect others back to us. Objects appear to be the color they reflect to our eyes.
Air is a mixture of gases, mainly nitrogen and oxygen, with small molecules that are far apart. Wavelengths of light may pass by these molecules without hitting them.
When they do bump a molecule, it absorbs some color and scatters some, spreading it out in all directions. Too little reaches our eyes for us to notice unless there is a lot of it. For example, so much scattered blue light in the atmosphere makes the sky look blue.
Art by: Keith Frawley