Basically, to use Flash Media Playback, you host your videos on your own website. The player itself is hosted on Adobe's servers.

To use Flash Media Playback is easy. Just go to http://www.osmf.org/configurator/fmp/, and fill in the values for your video. Adobe will generate the code for you, and you just drop it into your website. Easy as pie!

You can see the configuration for this video to see how it works from this screenshot:

Flash Media Playback Setup