Hello, suppose that an acid is HA and its conjugate base is A-. An acid is the (more) protonated form of the common anion, and the conjugate base is less (or not) protonated one.
For example, [itex]H_3PO_4[/itex] is an acid, and its conjugate base is [itex]H_2PO_4^-[/itex]. [itex]H_2PO_4^-[/itex] may be another acid, yet less powerful than the previous one, for its conjugate base, [itex]HPO_4^{2-}[/itex], which is a stronger acid than [itex]PO_4^{3-}[/itex]
Hope you got what conjugate acid/base pair means.