What are conjugate acid-base pairs?

All acids have a conjugate base. All bases have a conjugate acid. Acids "donate" ##H^(+)## when they react. This is most easily seen when they dissociate in water:

##H_2SO_4## + ##H_2O## => ##HSO_4^-## + ##H_3O^+##

In this example, sulfuric acid (##H_2SO_4##) is an acid because it "donates" ##H^+## to the water. It becomes the hydrogen sulfite ion (##HSO_4^-##) which is the conjugate base of sulfuric acid.

The same idea applies to a base:

##NH_3## + ##H_2O## <=> ##NH_4^+## + ##OH^-##

Ammonia (##NH_3##) is a base because is "accepts ##H^+## from water to come its conjugate acid, the ammonium ion (##NH_4^+##).

This video gives an overview of ; the second half is about conjugate pairs:

Simple, easy to understand can be on this site http://www.chemteam.info/AcidBase/Conjugate-Pairs.html