To unlock the Metal Region, you need to talk to the Swordswoman in the Forgotten Garden. (Meaning, you can't access the Metal Region until after you learn about the Forgotten Garden from the maid in Rizolt City.)
The Metal Region is a dungeon consisting entirely of "metal" monsters - monsters that are so strong, you can only kill them with critical attacks.
The great thing about metal monsters is that, when you do kill one, you get a TON of experience - so if you want to raise your character's levels, this is the place to do it.
The Swordswoman who first tells you about the Metal Region says you need to be around level 25 to enter, and while that's technically true, there are two parts of the region that are behind locked doors - a level 100 region, and a level 300 region, and each of these doors cost 1,000,000 gold to unlock, every time you enter the region.
So, feel free to explore the first screen of the Metal Region at any time (there are a few decent treasures on the first screen), but if you plan on doing any serious grinding here, you really want to plan ahead and at least be ready for the level 100 area before unlocking that door.