Okay, here's the non spoiler ambiguous thing: go back to the surface and walk around to both sides of the map and see what you can find. Just don't fall too far into any large chasms because they're very, very deep. As for the underworld: keep digging. For the first boss, maybe you can find something to do with those lenses at a demonic site. If I was you, I'd focus on killing my first boss (gold armour is well and truly sufficient for the first boss) and look for corruption. After digging for a while you'll find yourself unable to do anything useful (and will probably get killed quickly) until you explore the surface some more.No, I just seem to be digging forever.
More specifically (not really spoiling anything): on the surface are the Dungeon (on one side of the map) and large chasms leading to Corruption. At the bottom of corruption you'll find shdaow orbs like Lukasz said. Smash them. To get through corruption you'll need a better pickaxe than gold (which you won't have yet) or an item from a particular NPC which will only turn up after killing one boss. Until you've done these surface things (except Dungeon) there's no point digging any further into the underworld, you're not going to survive and you're not going to be able to do anything worthwhile down there.