Skin Effect in AC circuit is the tendency of the current to crowd toward the outer surface. This results in a current density that is greater near the outer surface of the conductor.
Skin effect is more relevant in AC system since it involves frequency. All electric currents generate magnetic fields that in turn can affect the current (this is the principle behind electric guitar pickups). In a direct current case everything is constant and so nothing seems to happen. With an alternating current, however, there is a delay in the magnetic field's response to the change in current and the 'old' magnetic field tends to push the current towards the outside of the conductor.
Skin Effect causes the longitudinal element of the conductor near the center of the axis to be surrounded by more lines of magnetic force than near the rim. This results in an increase in inductance toward the center.
Skin Effect increases the AC resistance of the conductor relative to the DC resistance. As the voltage drop in all wires is the same, a larger portion of the current flows through the outer conductor layers causing an increase of the effective resistance.
The decreased area of conductance causes apparent increase in the resistance. At 60Hz, the phenomenon is negligible in copper sizes #2 AWG and aluminum sizes #1/0 AWG and smaller. As the conductor sizes increase, the effect becomes more significant.
As the frequency increases, so does the effect until at very high frequencies the entire current flows in a very narrow skin on the conductor--hence the name.
Skin Effect contribution for round conductors at 60 Hz can be approximated using the following formula:
Ycs = 11.18 / (Rdc^2 + 8.8)
Where Ycs = Skin Effect expressed as a number to be added to the dc resistance
Rdc = dc resistance of the conductor in micro-ohms per foot at operating temperature