Hope this helps - there are two working electrodes (an anode and a cathode). The third electrode is a reference electrode to provide an exact potential to the instrumentation (e.g. Ag/AgCl or Calomel).
A potential is applied to the working electrode (constant potential in the case of basic amperometry). This provides the energy needed to drive the electrochemical process of interest. The zero potential is set by the reference electrode. If currents greater than a few microamps are going to be measured, a three-electrode system is needed. This is necessary because high currents will cause changes in the potential of the reference. The third electrode is the counter electrode. It acts as an electron source/sink. Current flows between the counter and working electrodes while potential is applied between the reference and working.
I suggest looking at books by Bard and Faulkner and edited by Kissinger and Heineman which cover this classical topic very well with pictures, math, circuit diagrams..