Upon introducing surfactants (or any surface active materials) into a system, they will initially partition into the interface, reducing the system free energy by:
# lowering the energy of the interface (calculated as area times surface tension), and
# removing the hydrophobic parts of the surfactant from contact with water.
Subsequently, when the surface coverage by the surfactants increases, the surface free energy (surface tension) decreases and the surfactants start aggregating into micelles, thus again decreasing the system's free energy by decreasing the contact area of hydrophobic parts of the surfactant with water. Upon reaching CMC, any further addition of surfactants will just increase the number of micelles (in the ideal case).
According to one well-known definition, CMC is the total concentration of surfactants under the conditions:
:if C = CMC, (d/dC) = 0
: = A[C] + B[C]; i.e., in words C = [single surfactant ion] , C = [micelles] and A and B are proportionality constants
:C = C + NC; i.e., N = represents the number of detergent ions per micelle