A buffer solution has the tast to keep the pH of a solution as stable as possible, even when strong acid or base are added.
In a buffer always are mixed toghether:
about the same amount of (weak) acid HA and conjugated base A-
The last one can, for example, be added in the form of the very soluble NaA.
The HA aims to catch added base and the A- aims to catch the added acid.
The more weak acid and conjugated base are toghether, the more strong acid and base can be caught and the bigger is the buffer capacity.
A rather concentrated mixture of a weak acid with its weak conjugated base
In a solution of a weak acid always:
[H3O+] = [A-] (those two are set free in equal amounts from HA).
In a buffer however, much extra A- is added, so in a buffer those two concentrations are no longer equal.
Adding to a buffer a littlebit of strong acid, the present weak base A- will catch (neutralise) that added acid.
Adding a bit of strong base to a buffer, the present HA will catch (neutralise) that added base.
From the well known formula for Ka, you must be able to deduce the so called