Just like 8mm projector, 16mm projector is just another type of movie projectors. It works the same way. It’s an machine that displays moving pictures on a projection display. It was popular in the past and it is still popular because you get that feeling of „past times“.
16mm projectors are economic alternative to 35mm projectors and films. They were used for displaying short comedies (around 20 minutes or less) and for projecting various cartoons that have been projected in theaters before that. It was mainly used in school and as a home system for entertainment before television became so popular.
Today, all those projectors can be bought and, of course, you can expect much better quality of picture. If you don’t want to buy it, then you can rent 16mm projector and still enjoy the feel of past in your home.