The concept of the idea is to extend the effects of the various biomes beyond just showing on the surface to also showing underground.
As biomes in general get more fleshed out, underground biomes could have a significant effect on what it's like to explore caves in different areas.
Just some random ideas for what different biomes could do underground with stuff that's already in the game:
High Rainfall Biomes - Moss patches grow across stone underground. Mushroom patches are more common. Water springs and ponds are much more common. Flooded sections of caves are semi-common.
Low Rainfall Biomes - Water springs and pools are very rare. Caves are sandy. Collapsing cave formations of sand are semi-common.
High Temperature Biomes - Lava springs and pools are much more common.
Low Temperature Biomes - Caves are icey. Frozen passages and iced over floors/walls/ceilings are abundant.
Tweaks to the code that generates the shapes of the different caves could be made for each individual biome as well. One biome could have small twisty passages, while another has large and open but isolated pockets, while yet another has sprawling underground vistas of lava and water flows.
(I find it surprising that nobody's suggested this yet, but I did a fair bit of searching both on the site and on google and failed to find anything similar)