One of the major advantages of streaming technology is to be able to play a movie directly from a website without having to download the whole file. The movie starts playing after a very little pre-buffering time. Forwarding or skipping through a movie in realtime is also possible without having to download the entire movie.
Additionally, a streaming-server is able to automatically reduce the quality of the transmitted content depending on your connection speed or push it back up to the maximum available resolution and framerate on a fast internet connection, without stopping the transmission.
Another benefit is, that streaming a movie provides a simple copy-protection of your content, as the user will not be prompted for downloading/saving the file.