So for example how can I use BVM to make my WIP FPS game better
To give the short and easy answer, BVM let's you add a scripting engine to your game.Take Unreal, all the game logic (AI in particular) code is put in separate scripts, rather than having everything hard coded in the core engine. This has a lot of advantages, and for Unreal the most noticeable is probably that it allows the end user of your game to make MODs of your game (the unreal MOD comunity is really huge, and it has done a lot for its popularity). This is one of the things that you can do with BVM. One point that tends to make most BVM users happy is that the language for the scripts is blitz itself, meaning that code that runs in blitz can run as BVM scripts (usually without even any modification).
For more, just have a look at the site and the trial version.