What is conjugate acid and conjugate base?

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Hint: We need to know that an acid is any hydrogen atom containing material ( molecule or ion) that can release a proton or hydrogen ion to any other substances, whereas a base is any substances (molecules or ion) that can accept a proton to any other substances to form the conjugate acid base pair.

Complete answer:
We can say that the members of which can be formed from each other mutually by the gain or loss of protons are called conjugate acids and bases pairs. The stronger acid and weaker base form one conjugate pair and the stronger base and weaker acid form another pair. Conjugate acid base pair can be:

H C l O_{4} \overset{}{⇆} H^{+} + C l {O_{4}}^{-}

H_{2} S O_{4} \overset{}{⇆} H^{+} + H S {O_{4}}^{-}

In the Bronsted–Lowry definition of acids and bases, a conjugate acid–base pair consists of two substances that differ only by the presence of a proton (

H^{+}

). A conjugate acid is formed when a proton is added to a base, and a conjugate base is formed when a proton is removed from an acid.
The chemical reaction presenting acid base theory can be written as:

A c i d + B a s e ⇄ C o n j u g a t e B a s e + C o n j u g a t e A c i d

In an acid–base reaction, an acid plus a base reacts to form a conjugate base plus a conjugate acid:
Conjugates are formed when an acid loses a hydrogen proton or a base gains a hydrogen proton.

Note:
If a conjugate acid is strong, its dissociation will have a higher equilibrium constant and the products of the reaction will be favored. The strength of a conjugate base can be seen as the tendency of the species to "pull" hydrogen protons towards it. If a conjugate base is classified as strong, it will "hold on" to the hydrogen proton when in solution and its acid will not dissociate.