The term "movie trailer" isn't a very good phrase to describe the previews that we see before movies these days, but at one point it was. Originally, these previews were shown after the feature film, as a trailer to the movie people had paid to see. However, folks weren't sticking around to catch these coming attractions, so they were moved from the end of a film to the beginning.
A lot has changed over the years though. For many people, going to the theater isn't only about watching the feature film; it's about going early enough to watch the previews as well. For some, the only downside is that they don't get to see enough previews for upcoming movies unless they see two or three movies a week. But with the Internet, it's possible to download movie trailers right to your computer to watch at your convenience.
Years ago, viewing a movie trailer online meant watching a pixelated, postage stamp-sized window which made it difficult to see exactly what was going on. Thanks to faster connections and bandwidth increases, it's now possible to download full-screen movie trailers in near-DVD quality. Many of these trailers that you can view online, you may not even have a chance to see in theaters or on TV.
Oftentimes, in theaters, you'll likely see movie trailers for upcoming big budget films starring big name actors, but no lesser known, limited release films. Thankfully, on the Internet, you can expose yourself to a wider variety of films that you may not have a chance to preview otherwise and watch them all without spending a dime on overpriced concessions.