Why are caves wet?

Purely terrestrial karst (limestone) cave passages can, and do, form in "phrearic" conditions, i.e. entirely full of flowing water, often under considerable hydrostatic pressure.

At least some karst caves found under the sea such as those around Florida developed above water at times of lower sea-level.

Topographical changes by glacial action - moraine dams - may raise the outlet level, drowning previously partly air-filled passages.