Why can you see a laser beam's path in the air?

Answer: Tiny particles in the air scatter laser light toward your eyes

The laser creates a solid beam that hangs in the air — A laser does make a narrow, straight line of light, but it emits light rather than a solid object. The beam seems to hang in the air because particles along its path redirect some light to your eyes. Without those particles, there is no visible column from the side.

Tiny particles in the air scatter laser light toward your eyes ✓ — You cannot see light traveling sideways; you only see light that enters your eyes. Dust, water droplets, and air molecules along the beam's path scatter some laser light toward you, so the path looks bright. In a clean vacuum, with nothing to scatter the light, the beam would not be visible from the side.

Your eyes respond more strongly to the color of laser light — Your eyes may find some colors brighter than others, but that only changes how strong the light seems once it reaches you. It does not make light visible from the side. To see the beam, light from the beam still has to enter your eyes.