Dungeons in Magience can refer to two things; Type A "Classic" dungeons and Type B "Maze" dungeons.
Type A "Classic" Dungeons
These are the dungeons most gamers think of when they hear the word; underground labyrinths, puzzle-like cave systems, and complicated monster-infested castles. Most Type A dungeons have a Spawn Point outside.
For many dungeons the average level of all players currently within the dungeon directly effects the strength of the monsters encountered, within a certain level range. Every dungeon has a level range, or "bracket". For example, if a dungeon has a bracket of levels 10-20, that means the monsters who appear can be anywhere from level 10 to level 20 in strength. A party whose average level is 12 will have monsters appearing around level 12. However, if a party whose average level is 45 enters a 10-20 bracket dungeon, the monsters who appear (if any) will be around level 20 and not any higher.
This is because monsters tend to be drawn to people with strength levels close to their own - lower level monsters will avoid strong players, and strong monsters won't waste their time on weak players most of the time unless the player gets in their way or they're a particularly aggressive type of monster.
For Type A dungeons, the dungeon is considered completed when the "Boss" is defeated. A "Boss" is the strongest monster in the dungeon. The level of the boss never changes, always remaining several levels higher than the highest bracket; to use the same dungeon as before, a level 10-20 bracket would have a boss monster around level 25-30 regardless of the average player level. Some dungeons can have an assortment of different bosses that might appear at random so a party that completes the same dungeon several times may fight a different boss each time. Most Type A dungeon bosses wait in a certain area and will not attack unless provoked. Boss monsters often guard or drop valuable treasures, and are always stronger than normal monsters of the same level - a boss of level 10 will always beat a normal level 10 monster. They are also worth ten times as much experience as a normal monster of equal level.
Type B "Maze" Dungeons
These dungeons are found in the field and are commonly referred to as "Mazes". Unlike Type A dungeons, these rarely have Spawn Points nearby and are usually open to the elements. It can sometimes be hard to tell when you've left the field and entered a Type B dungeon unless you pay very close attention. Maze dungeons can be city ruins, enchanted forests grown into complicated patterns, or even an empty plane that's been warped by magic.
Type B dungeons also have level brackets, but the brackets can be broken by monsters who tend to wander so they can actually be more dangerous than Type A's.
Boss monsters in Type B dungeons tend to roam the dungeon itself and can be hard to predict. Often, if the boss is a sentient creature its treasure will be hidden within the dungeon proper and can be found by grabbing a map off the boss corpse. Of course, this means that every so often a party can accidentally stumble onto a boss treasure without actually fighting the boss itself.
Sometimes a dungeon can be "Cleared". Most adventurers consider these dungeons "dead" or "grind zones ", since they don't have as much treasure to be obtained. When a dungeon is cleared, it no longer has a boss monster within its perimeter to defeat, though monsters within its level bracket will still appear.