What is skin effect and proximity effect?

Skin effect is the tendency for high-frequency currents to flow on the surface of a conductor.

Proximity effect is the tendency for current to flow in other undesirable patterns—loops or concentrated distributions—due to the presence of magnetic fields generated by nearby conductors.

In transformers and inductors, proximity-effect losses typically dominate over skin-effect losses.

In litz-wire windings, proximity effect may be further divided into internal proximity effect (the effect of other currents within the bundle) and external proximity effect (the effect of current in other bundles).

Skin Effect: When a DC current flows through a conductor, current is uniformly distributed across the section of the conductor. On the other hand, when an AC current flows through a conductor, outer filament of that conductor carries more current as compared to the filament closer to its center. This results in higher resistance to AC than to DC and is known as skin effect.

Proximity Effect: The alternating flux in a conductor is caused by the current of the other nearby conductor. This flux produces a circulating current or eddy current in the conductor which results an apparent increase in the resistance of the wire and; thus, more power losses in the windings. This phenomenon is proximity effect.  

Skin Effect
Suppose there Conductors from which Alternating Current is flowing. Now what happens is due internal flux linkages Current density near the outer surface area is higher and it is gradually decreases toward the axis of the conductor.
This Non-uniform current density causes higher current flows near the surface of the conductor than the core for Alternating current. This Effect is Called “Skin Effect”.
Skin Effect becomes higher as the Frequency increases. Also due to skin effect DC resistance of the conductor becomes higher.
Skin Effect is absent in Direct Current (DC).
Proximity Effect
Current density in Conductor depends on internal magnetic flux distribution. Proximity means adjacency. So, Proximity effect present at when two Alternating current carrying conductors are near to each other.
Now what happens is Magnetic flux produced by both conductors” A & B” links with each other. That will change internal magnetic flux distribution such that for a conductor “A” current density near to the conductor “B” decreases and on the other side Increases. So, current in Conductor “A” will be less on Conductor “B” side and less on other side.
This Effect is called “Proximity Effect” in Power System. Proximity Effect will also increase effective Resistance of Conductor when Alternating current flows from it.