For most cases, the feature is there because it is fashionable. The customer saw it on a site and loved it, the site developer just learned how to do it, so they both insist on doing it, and rejoice.
In some cases, it is a really useful tool for saving bandwidth. An example is Image search on Bing: images do use non-negligible bandwidth. Images will be downloaded "on demand" and the page virtual length is effectively infinite (at least, as infinite as the Internet supply of pictures of cute kitten).
The technique is sometimes dubbed "infinite scrolling". Whether it is a good idea is debatable and debated.
What the content providers do of the information is unknown. Methinks they make some statistics, if only to optimize the amount of background preloading for the infinite scrolling feature. In the case of an image search, the terms used in the search box are much more damning to you than your scrolling behaviour anyway.