As a broad overview:
It is typically used to calculate the resting membrane potential (voltage) of a cell. In excitable cells there are two principle forces in play, concentration and electrical charge. The nernst takes both into account.
By taking the natural log (ln) of a given positive ion concentration outside divided by inside (opposite for chloride or neg charged ions) and multiplying that number by the gas constant R and the absolute temperature in kelvins and then dividing by the faraday constant. If the ion is negative then also divide by negative 1. Answers are typically expressed in mV.