Equilibration buffer provides a condition to ensure that the target molecules interact effectively with the ligand and are retained by the affinity medium as all other molecules wash through the column.So the buffer pH and ionic strength at optimal condition are responsible for this ligand-molecule interaction.I hope this will help you.
Equilibration buffer is made to equilibrate the system (here it's a column) with defined condition supposed to favour the first step in affinity chromatography which is to adsorb the molecule of interest onto the solid matrix. Equilibration buffer has also to be compatible with the stability of the molecule of interest during the process.
Equiliberation is used not only in affinity purification but in other lab procedures as well. In case of affinity purification it is used to avoid any shock to the resin just before application of your sample. Suppose you are trying to get something out of cell culture medium, your equiliberation buffer must contain cell culture medium. It would promote the affinity binding of the desired molecules.
All the answer is correct as said above authors, the equilibration buffer is gives more affinity to the desired molecule along with ligand and receptor interaction...