In Deepworld, the underground is made up of any area that has background earth (including open areas that show the cave lattice background). Dig in to shelter from acid rain, build bases and bunkers, tunnel from cave to cave: the underground offers endless opportunities.
Earth in the underground is layered and becomes progressively harder as you dig deeper. Raising your mining skill levels will allow you to mine further down.
Most world maps will be roughly 2/3 underground and 1/3 sky. The exception is the deep biome, which is entirely underground.
Ores abound at all layers of the underground in all biomes, as do dungeons and bunkers with precious chests of loot or rare paintings and objects. Such structures also offer unlimited building materials that you can scavenge and reclaim, and house things like unrepaired teleporters, ecological machines and their parts, and even an array of slightly-used items and devices for your home, office, or dungeon-in-progress. Networks and clusters of caves offer up all the important goodies like onyx, diamonds, and crystals. The underground is home to just about anything you could want!
The underground is also the only place you'll find maws and culverts, which drop various monsters and enemies. There are other dangers as well -- watch out for stalagmites and stalactites, pools of acid and lava, and randomly-spawned mobs lurking around every corner.
If you have at least perception skill level 3, the minimap will display explored vs. unexplored areas. Each area is 20x20 blocks. Moving into an unexplored underground area will give you XP, and will cause the minimap to change that area to a lighter color.
Although exploring the sky will also cause changes in the minimap, and will contribute towards the percentage of the world that's explored, it will not give XP and doesn't count towards achievements or crow rankings.
The underground has always been part of Deepworld. I mean, c'mon. Look at the name. Deep. World.