.flv stands for FLash Video. It's a file format able to contain video data. The main difference with other formats (ogg/ogm, mkv, avi, ...) is that the flash player that browsers often use to play flash animations is capable of reading this format, which makes it suitable for videos viewable on the web.
MPlayer (on linux and windows) is a free software program that is capable of reading .flv files alone, without any browser and without the flash player.
If you are using a Macintosh computer, a free program called VLC will do a great job playing these files without the need of an internet browser.