It's because we can see light if and only if it reaches our eyes. A beam of light travelling from a source to a screen is invisible to us because light generally travels in straight lines and it doesn't reach our eyes, unless the source emits rays in the direction of our eyes. But, when we look directly into the source, our eyes intercept the rays coming from it and hence we see it. Also, we can observe a spot on the screen where the beam strikes because after striking the screen, the light gets reflected in all directions.
