RC, All organic matter will decay and biodegrade back to an elemental form. Bacteria is one of the primary digesters that cause decay (rot). There are many types of bacteria, but in a pond we pretty much have either aerobic or anaerobic. Anaerobic bacterias live and do their thing in the absense of oxygen and are slow to consume organic matter, if at all. Aerobic bacterias require oxygen and can consumes organics very rapidly.
By adding an aeration system, you supply oxygenated water to the lowest parts of a pond to allow the faster working aerobic bacterias to thrive.
Let's take the aeration step a little further and apply it to leaf debris--- Leaves fall into the water and get tightly packed over time. Aeration will provide oxygenated water to the surface of that but not into the leaf depth very far. When something like a rake or fish or even walking disturbs and mixes the leaves, it not only brings oxygen to deprived areas, but allows a fresh, unpopulated (by aerobic bacteria) substrate for more aerobic bacteria to colonize and consume the leaves----further speeding the process.
As to where the debis goes, well eventually back into the water column as a nutrient or as a base/trace element to be available to other plants and animals to grow.
I'm no expert on this by any means. I have tried to simplify an extremely complex process to make it a little easier to understand and digest.
I had to turn off the aeration in my pond last year. I get roughly 15-20 tons of hardwood tree leaves going into my inflow areas. With aeration from day one of building my pond, the clay lining was exposed in every area. After only six months without aeration, packed leaf debris was already in excess of 6 inches thick everywhere.
