"Sodium" refers to the element sodium. "Pareth-" denotes a PEG ether of an alkanol. The number after "Pareth-" indicates the average number of molecular units -CH2-CH2-O-.
"Butyl" usually designates butanol (1-butanol or n-butanol) as the alcoholic component or, in general, a saturated hydrocarbon chain with 4 carbon atoms. Phosphates are salts or esters of phosphoric acid.
Sodium C13-15 Pareth-8 Butyl phosphate is a substance which is used in cosmetic preparations where it acts as an emulsifier (surface-active substance which is used in cosmetic preparations as an auxiliary agent in order to combine two immiscible liquids - e.g. oil and water - to an emulsion).