critical micelle concentration
Think of a party where guests first spread out along the walls, but once the walls are full, latecomers start clustering in the middle of the room. For a surfactant in water, the walls are the surface and interfaces; once those are saturated, additional molecules cluster into micelles. The concentration at which this clustering begins is the critical micelle concentration, or CMC.
Below the CMC, added surfactant goes mostly to the surface and exists as free single molecules (monomers) in solution. At the CMC the surface is saturated and any further surfactant aggregates into micelles, so the free monomer concentration stays almost constant beyond this point. This sudden change shows up as a kink in plots of surface tension, conductivity, or solubilising power against concentration, which is how the CMC is measured.
The CMC is a defining property of each surfactant and is lowered by longer hydrophobic tails, added salt, and certain temperatures. It matters pharmaceutically because solubilisation, foaming, and detergency only switch on near and above the CMC, and because injectable formulations diluted below the CMC in the bloodstream lose their micelles. The caveat is that the CMC is a narrow range rather than a perfectly sharp point, and reported values depend on the method used.