A Guild Dungeon is a special type of time-limit dungeon that can only be opened and entered by a Guild member, usually a Guild Leader or Guild Chief Officer. It's usually comprised of multiple floors with many mobs to kill, and since requirements for clearing tend to be rather high, squad preparation is a must.
Guild Dungeons can be only be accessed after being opened using a key that is only obtainable by a guild leader, from [Pointry], for a certain sum of guild points (Guild Points). Once the dungeon is opened, an instance is created which lasts for two hours and is only accessible to members of the guild that opened it. A certain guild level is required to in order to use the access keys.
Training Center isn't a Guild Dungeon per se, but it's close enough to merit listing here and has similar drops to Guild Dungeons, especially Star Stones.
Reward Boxes for completing Guild Dungeons are mailed to the Guild's Leader upon dungeon completion. The leader can then choose to distribute those boxes as he/she sees fit. They are typically split up evenly among participating players.