You'd be digging along, and dig into the side of a small existing cave. Or maybe a larger cavern. And, of course, some of them would be occupied, probably by things that would not like the intrusion.
And some caves might have special features of their own. Things that arent REQUIRED by the game, but might make things more interesting. Like awesome natural formations, that would give a huge happiness hit when a dwarf sees them. Or a natural sinkhole pit trap, that sometimes drops surface animals to their death (Instant free meat, bones, and skins.). Nothing game breaking, just some random bits of strangeness/usefulness/excitement