A swallow hole is a place where the ground literally swallows up a stream. Swallow holes (which some people call potholes) are on the top surface of rocks that allow water to pass through. Mostly commonly these are limestones. The water dissolves the limestone, making the hole bigger.
Most swallow holes are the entrances to cave systems.
The place where the water comes out again is a spring (and geographers call a resurgence). That will be at, or close to, the bottom of the rock.