The FLV extension identifies Flash video files. By using it on Youtube and similar sites, it has become the standard format for streaming Internet video.
The format was developed by Macromedia and is being further developed by Adobe today. It's a proprietary format, but it's also made available to other developers.
Like MOV, FLV is a container format. The files contain a video and audio stream as well as metadata. The included audio and video data may be encoded using various compression techniques. Which ones are depends on the desired compatibility with the Flashplayer plugin. With higher versions, other methods are available that also support HD resolutions.
Any browser with Adobe Flashplayer plugin can play FLV files.