You can start clearing the Treasure Dungeons (Abandoned Mine B1, Abandoned Mine B4) once you hit level 50. The Abandoned Mine B1 can be cleared 10 times a day, while the Abandoned Mine B4 can be cleared 5 times a week. These dungeons require a key, which can be obtained by analyzing Rusted Keys in Tria for 100,000 Mesos (or more if you do it more than once a day). B4 requires at least 4 party members.
B1 possible rewards are: Blue Crystal, Green Crystal, Lapis Master Snare (pet trap), Fusion Stone Dust (for pet fusion), Crystal Fragments, and Tier 1 gemstones.
As for the treasure dungeons themselves, you get points from collecting these blue things from opening chests. Some of the chests will actually be monsters that will attack you. These points do not actually do anything from what I can tell, but I may be wrong about that, so please let me know if I'm wrong. For the B1 (solo) treasure dungeon, you can simply find the right path and fight the boss. For the B4 (4 man party) treasure dungeon, you will have to split up into two groups, with 2 people going left, and 2 people going right. From there each group will have to pull levers and reach the bottom to remove the water barrier and eventually fight the boss.