Detergents are basically chemically defined as the ammonium or the alkyl benzene sulfonate salts of a long chain of carboxylic acids.
A synthetic detergent is basically a synthetic substance and is an effective cleanser that functions equally well as a surface-active agent either in hard or in soft water.
They are usually made up of surfactants and are effective because they have an amphipathic structure which means that one side of the compound is hydrophobic which will avoid water whereas the other side is hydrophilic which will easily attach to water.