The Beneath is a network of very deep caves, directly below the Overworld.
This dimension is balanced around mid to late Primitive Age. It's more dangerous than the surface, so we recommend a full set of bronze armor and a metal shield as a minimum, as well as plenty of food, water, and other tools.
It differs from the usual Nether experience in a few ways:
To travel Beneath, simply stand on overworld bedrock for a little while. To get down to the bedrock, you'll have to either break through the Hornfels layer with Explosives or Steel+ Tools, or find a cave with the more brittle Keratophyre.
To return, stand directly below ceiling bedrock in the same fashion.
It's a good idea to make a note of where you entered, so you can return to the same place in the overworld whenever you're ready to leave.