Here's why:
* Light travels in straight lines: The projector's beam is a concentrated stream of light.
* Air particles scatter light: The air between you and the projector is filled with tiny particles (dust, water vapor, etc.). When the light from the projector hits these particles, it gets deflected in all directions.
* Scattered light reaches your eyes: Some of this scattered light travels towards your eyes, allowing you to see the beam.
The brighter the projector beam and the more particles in the air, the more noticeable the beam will be. This is why you might see the beam more clearly in dusty or smoky environments.