The combination of a glass electrode and reference electrode can be thought of as a battery with high internal resistance. Thus, you cannot measure the difference in potential accurately if you connect it to an ordinary potentiometer (voltmeter) as-is. You need an amplifier with high input impedance. The indicator of the pH meter has such an such amplifier built in, and allows adjustment. A dial for adjusting asymmetrical potential, a dial for temperature compensation, and a dial for adjusting sensitivity are indispensable for the indicator of a pH meter. The dial for adjusting asymmetrical potential is intended for adjusting readings on the pH meter so that they will correspond to the pH values of the reference solution when you immerse the electrode in the reference solution, moving to zero point of the amplifier electrically.
The dial for temperature compensation is provided for compensating for variations of electromotive force of the glass electrode per 1 pH due to temperature and for adjusting so that the indicator will indicate the correct pH values irrespective of temperature. However, this adjustment is automatic with any pH meter that has a temperature-compensation electrode (automatic temperature compensation). Therefore, such a pH meter would usually not have a temperature-compensation dial. Instead, it would have a dial for adjusting sensitivity.
This dial is for adjusting the sensitivity of the amplifier so that it will correspond to the electromotive force of the glass electrode per 1 pH of at a certain temperature. Its electrical action is not different from that of the temperature-compensation dial, though its adjustment range is rather narrow.

Difference in asymmetry potential

A glass electrode has an internal electrode, and it has an internal solution with of a pH of 7. If you immerse the electrode in a solution with a pH of 7, both the solution inside and that outside electrode membrane have pH of 7. Therefore, the difference in potential should be 0. However, a certain difference in potential exists there. This is generally called the asymmetry potential. The asymmetry potential can vary depending on distortion and shape of the glass due to limits of precision in processing and the composition of the glass. It may be caused by contamination of the internal solution of the reference electrode. Moreover, when an electrode membrane is dry, the difference in asymmetry potential becomes large, causing errors in measurement. Therefore, the tips of new electrode are covered by protect caps, and those protect caps are keeping of sponge with water. Also, remember that the difference in asymmetry potential is generally within ∓0.5 pH.