Layering is a form of propagation where the desired material is not removed from the mother plant before it has formed roots.
This utilizes a plants natural abilities and tendency to form new roots if it falls over or if a limb touches the ground. This can be accomplished by bending the desired material to the ground and covering a portion of it with soil. Ensure it stays moist and in a couple of months it can be removed from the mother plant once it has formed roots and transplanted into a suitable container.
Air layering is where one wraps a suitable tree limb with a growing medium like moist sphagnum moss covered by plastic to seal in the moisture and prevent it from drying out. Once again after a couple of months the limb can be removed once suitable roots have formed.
This differs from cuttings in that the potential propagated material remains connected to its host during the root formation process. This ensures that the necessary nutrients etc. still circulate during the root forming process.
The principles are quite simple but the execution may need refinement for some species of trees. We typically wouldn't layer our bonsai as it can take months and is unsightly.
There are plenty of resource on you-tube and elsewhere on the specifics for the species you are interested in propagating.
