Micelle

The critical micelle concentration is the minimum concentration at which the emulsifiers in a detergent will coalesce in to membrane structures of globes, rods or sheets with their hydrophobic (water hating) ends on the inside of the membrane and their hydrophilic (water loving) ends on the outside such that hydrophobic oily residues can be emulsified inside these membrane structures.  Micelles are further elaborated on below.  If you are below the critical micelle concentration, you do not have effective emulsifying of oily residues.