There are 18 Group Dungeons, five in each faction zone, one in Coldharbour, and two in the Imperial City. These are designed to be explored with a group of four players maximum. The enemies inside will be of a much greater difficulty than those in Public Dungeons, and unless you are in a group, you'll be facing them by yourself, because these dungeons are instanced—meaning you won't see anyone not grouped with you when you enter.
Ten Group Dungeons also have Veteran Dungeon variants. These become available once you hit Level 50 and are granted Veteran Rank 1 (1). These usually use the same, or similar maps, but with different, higher level enemies. They are understandably much more difficult, and can earn you numerous Veteran Dungeon Achievements. The quests in all Veteran Dungeons (except for White-Gold Tower and Imperial City Prison) continue the storyline established previously in the Normal level Group Dungeons.
These dungeons can be added to your map by talking to members of the Undaunted in the taverns of the major cities of each zone, and can then be teleported to directly from the Wayshrine fast-travel system. All Group Dungeons can be discovered this way, making them the only places within other Alliance territories that you can visit before reaching Level 50. If you have not previously discovered a particular dungeon, the wayshrine for that dungeon will be added to your map upon acceptance of the corresponding pledge.
Min Level refers to the minimum level of enemies within the dungeon, and therefore the recommended minimum level of entry. Note however that it is still possible to enter before this level. When entering a dungeon, all enemies, minibosses and bosses will be scaled to match the level of the group leader. If the leader is below the minimum level of that dungeon, all enemies will be at the minimum level for that particular dungeon.