1. Most movies are made in cinemascope mode. Here the screen is much more wider than a typical tv screen. Some movies are also made in 16:9 or similar ex: Zero dark thirty, most 3d movies etc. But most of the movies made are in cinemascope mode.
2. So how do you take a movie made for wide screen and show it in a screen that is narrower? One way is to crop/compress it - but that means you lose either some part of the image itself or distort the image (unnaturally tall, thin sticky figures).
Another way is to keep the width as it is, but still show it in a smaller screen - without distortion. The only way to do it is to make the height smaller - here they are not just reducing the height but making the whole image smaller uniformly until the width fits in the screen but by then the height has reduced so much that there are black bars on top and bottom.
3. Only the projector makers can tell why they make projectors that by default show in 16:9. It could be because if you want to show regular tv content (16:9) on cinemascope, then the image would be become too small. So i guess 16:9 is a good compromise.
4. Folks who have answered above have rightly pointed out that the best format to watch something in is the format that it was made in. That way you don't miss anything by way of cropping or distortion. But if you think you can live with some distortion (or loss of content at the sides) but want full screen absolutely, there are settings on the player and the PJ that can do this. Just read the manual of your player/tv/PJ