Whenever you see the word detergent or soap it refers to a water-soluble compound which helps dissolve non-water soluble compounds (like dirt and oils.) Detergent, unlike soap, does not form soap scum when used with salt containing hard water. Typically these types of molecules have the form of having two ends: a water soluble polar or ionic head and a long organic chain tail. The simple principle is that like dissolves like. That is, that the water soluble end has similar polarity to water and allows the molecule to dissolve in water while the organic carbon chain helps dissolve other organic molecules and oils. This process has been studied in detail by chemists. We call these types of molecules surfactants, and you can look up more about how the work in chemistry textbooks or on the Internet.