Both "Kill X of Y", and "Reach Depth X" are unlocks, which is a form of content gating, if you click on them it will tell you what it is unlocking but basically a fairly large and varied amount of things only start spawning once you have unlocked them.
So if we take a couple of examples,
"Kill 40 of Water Esper" unlocks Clockwork Probes, which are a harder form of enemy and which will initially spawn in...I think the grasslands.
"Reach Depth 2 in Desert" unlocks Copper, prior to doing the unlock no caves you explore will contain copper, afterwards it will be obvious and everywhere.