Where do waters from natural waterfalls come from?

The answer is simply natural subsurface storage. Almost all rainfall reaching the ground infiltrates into a temporary subsurface store, and most of what we observe in the river has drained from this subsurface store (rather than only flowing overland, as outdated text books would suggest). In circumstances where there is no virtually no soil overlying near impermeable rock, then drainage from this store to a river will cease within a few hours. Where a soil is present, but no permeable regolith (i.e., weathered rock, sediments, glacial drift etc) or permeable rock, then drainage can continue for several days (or even weeks) after rainfall. Where permeable soil and permeable regolith are present (but no rock aquifer) then drainage and hence riverflow would flow for weeks (or even months). Lastly where the soil is overlain by a permeable rock (an aquifer: i.e., a subsurface media which can store and transmit water) then drainage and riverflow can continue for months (and sometimes years) after cessation of rainfall. Within this sequence of scenarios, it is the natural subsurface storage that is increasing to sustain riverflow (and waterfalls) for longer and longer periods.