On a DVD-Video disc, the Video Manager Group, or VMG, is a special VTS that generally serves two purposes. Most of the time, the commands run when a DVD starts playing are contained in menus of the VMG.
More importantly, the VMG is a link between other regular Title Sets. Since a command in one standard VTS can't directly reference a menu or Title in another standard VTS, the VMG is used as a sort of relay point. It has a special table of titles that contains information about every title in every VTS. Since every VTS can reference the VMG, a menu command from normal VTS can point to a menu in the VMG, which in turn can point to a title from a different VTS. This is often required when all the menus are in a single VTS, but the titles are spread across several.
The VMG includes 2-3 files. It always has files called VIDEO_TS.IFO and VIDEO_TS.BUP that contain menu instructions. If there's video in the VMG, which is commonly where things like studio logos and legal warnings are stored, it will also have a VIDEO_TS.VOB file.