A conjugate acid is the product of a basic hydrolysis while a conjugate base is the product of acid hydrolysis.
For example, when an acid, such as HCl 'reacts with' water it will produce H3O+ and Cl-. The H3O+ ion is the conjugate acid of the Brønsted-Lowrey base, water. And the Cl- is the conjugate base of the acid, HCl.
A buffer is a solution containing a know concentration of a weak acid and a similar concentration of its conjugate base. For example, a solution containing 0.0010 M HF (a weak acid) and ~ 0.0010M F- (which could be made from a soluble salt such as NaF. Similarly, a basic buffer could be made from a weak base plus its conjugate acid. For example, NH3 + NH4+.
The function of a buffer is that the solution can absorb some strong acid or strong base being added to it without dramatically affecting the buffer solution's pH.
