When a channel type that is selective to one species of ion dominates within the membrane of a cell--because other ion channels are closed, for example--then the voltage inside the cell will equilibrate to the reversal potential for that ion (i.e. assuming the outside of the cell is at 0 volts). For example, the "resting potential" of most cells is close to the potassium reversal potential. During a stereotypical action potential, the small resting conductance mediated by potassium channels is overwhelmed by the opening of a large number of sodium channels, which brings the membrane potential close to the reversal potential of sodium. When a cell has significant permiabilities to more than one ion, the cell potential can be calculated from the Goldman-Hodgkin-Katz equation.
More at: electrochemical potential -- cell potential