Salicylic acid is a relatively polar, poorly aqueous soluble material.
The salt form however is quite water soluble. By changing the pH of the aqueous buffer you are able to alter the ratio between the ionized and unionized form of the acid. Since it is the unionized form which is extracted into the organic phase, the fraction extracted will vary with pH of the aqueous solution. The definition of Ka can become useful. This can be converted into a straight line equation by taking the reciprocal of both sides of the equation.