After digging a decent amount, you must have almost guaranteed came across a network of tunnels, referred to as "Caves" in Terraria. They are very plentiful with both monsters, urns, chests and most importantly, ore.
Here in this image, we can see the highly sought after Platinum. If you had another world type, It would be instead called Gold and be displayed as such.
Chances are also, that you haven't managed to find one of these glowing hearts yet. They are extremely sought after by new players as they are capable of permanently increasing your max health by 20+ each use.
In this case, I found my first heart in an underground mushroom "Biome".
Along with hearts, are the also quite-rare Golden Chests. They are like regular chests but boast much better loot.
The game (along with most other RPGs/adventures) also features mana for spellcasting. To increase your maximum mana pool, go up on the surface at night and collect "Fallen Stars". They come down from the sky every now and then at night and then disappear when It turns day.