Theme videos are just platform or gameplay videos with with artwork added to enhance the video. You just use them if you prefer it over standard gameplay videos and there is a setting in BigBox you can check to use them over non-themed videos. If you downloaded them from within the LB UI them LB will name them correctly and place them on the right folder.
Badges are just little badge decals currently only available in LB. It puts a small icon next to the game image. In LB under badges you can see what badges are currently supported to be shown. Things like if the game is a Steam game (as well as others), multiple discs, favorites, if it is an installed game, and some others. So it is just an icon to give you a quick reference about the game.