Ion-selective electrodes are electroanalytical sensors which uses the principle of potentiometry, or measurement of cell potential by measuring activities of ions in a solution (De Marco & Clarke, 2009). ISEs exhibit a certain degree of selectivity making it an effective method in quantifying electrolyte concentration in biologic samples (Štulı́K, 2005).

De Marco, R., & Clarke, G. (2009). ELECTRODES | Ion-Selective electrodes. In Elsevier eBooks (pp. 103–109). https://doi.org/10.1016/b978-044452745-5.00848-0

Štulı́K, K. (2005). ION-SELECTIVE ELECTRODES | Overview. In Elsevier eBooks (pp. 493–498). https://doi.org/10.1016/b0-12-369397-7/00291-0

Realyn Marabe I will try to give a simple explanation. Ion selective electrodes (ISE) are based on potentiometric measurements, that is, potential difference in a two-electrode cell. In the cell there is a reference electrode and the ESI, which is an indicator electrode. The ESI is capable of interacting with the analyte selectively through mechanisms that are generally based on a selective membrane, but there are also adsorption mechanisms, for example on nanomaterials, of all the membrane mechanism is the most common in commercial electrodes. When the ion diffuses through the selective membrane, a change in the potential difference measured with respect to the reference electrode according to the Nernsnt equation occurs because the activity of the ions changes. In practice, the Nikolsky-Eisenman equation is used, which takes into account interfering ions. There are different types of selective membrane that can be solid, liquid, gas permeable and enzymatic. In the article given bellow you can find the fundamentals of potentiometry and ion-selective electrodes, you can use the browser's translator to see it in English. Regards!

https://ojs.latu.org.uy/index.php/INNOTEC/article/view/626/1405

the key mechanisms behind how ion-selective electrodes (ISEs) quantify electrolyte concentrations in biological samples:

Overall, an ion-selective membrane and the resulting charge separation creates a measurable, steady-state electrical potential proportional to the concentration of a specific free ion in solution. This enables quantitative electrolyte detection in clinical samples down to parts per million levels or below.

All the previous answers are correct. However, I would add a fundamental concept to measure biological samples: ionic strength interference. Since the ion behaviour in water is also affected by the proximity of any other ion, the total ionic strength of the solution - i.e. the interference generated by ions and their respective charges, even identical ions - will change the response. This interference depends on the concentration of every ion species, thus the use of TOTAL ionic strength to correct measures of concentration. How to avoid or null this interference? You can use ionic strength buffers to standards and samples and standard addition, which is a little different in mathematical terms from the standard addition in spectrophotometry. I can develop the concept if you need. Nevertheless, if you want to measure only activity and not concentration, you do not need to use standard addition or ionic strength buffers.