"Potassium..." refers to the element potassium, "alkyl" describes a mixture of alkanols (alcohols derived from saturated hydrocarbons). The prefixed numbers "C x-y" indicate the range of carbon chain lengths (here C9-C15) of the alkanols. "Phosphates" are salts/esters of phosphoric acid.
Potassium C9-15 alkyl phosphate is a substance which is used in cosmetic formulations. It acts as a surfactant (washing-active substance; improves the even distribution of the products during application).