Self Induction:
When the current through a coil changes with time, due to the change of the magnetic flux linked with the coil itself, an emf is induced in the coil which opposes the change of current through it. This phenomenon is known as Self Induction.
Mutual Induction:
When the current through one of the two neighboring coils changes with time, an emf is induced in the other coil due to the change of the magnetic flux linked with it. The emf so induced in the second coil opposes the change of current through the first coil. This phenomenon is known as Mutual Induction.
The mutual inductance that exists between the two coils. It can be greatly increased by positioning them on a common soft iron core or by increasing the number of turns of either coil as would be found in a transformer.