What do you need to know?

This is a technical page. What you have to know at least is:
the electrode consumes oxygen, so you must stir to obtain reliable results! 
the electrode is calibrated with the potentiometer to 100% by moving it through well aerated water (shaking or bubbling through)
the electrode is sensitive for temperature differences, so you should measure everything at the same temperature, to obtain reliable results.

Operation of the oxygen electrode

The O2-electrode consists of a KOH (0,1 M) filled space with two poles, which space is confined by an O2-permeable membrane (see figure below).  One pole consists of lead (Pb), the other of silver (Ag), and brought together in the KOH solution in the space behind the membrane, a galvanic cell is formed with potential differences up to ±800 mV. When no O2 diffuses through the membrane, (submerge electrode in Na-sulfite), no current will pass the system and the potential over the input of the meter will be 0 mV. See animation. When the electrode is held in air or oxygen containing water, O2 diffuses through the membrane, which will be reduced at the silver pole:

                      2 Pb ð  2 Pb2+ + 4 e–
 2 H2O + O2 + 4 e– ð  4 OH–
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 2 Pb + 2 H2O + O2 ð  2 Pb(OH)2

and/or:

          2 Pb + 4 OH–  ð   2 PbO + 2 H2O + 4 e–
 2 H2O + O2 + 4 e–   ð   4 OH–  
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               2 Pb + O2  ð    2 PbO


The required electrons come from the lead pole, leaving lead-ions, and run through the wires and the potentiometer to the silver pole. The OH-ions formed at the silver pole diffuse via the electrolite (KOH) to the lead pole and will combine with the Pb-ions to lead hydroxide and/or oxide. See animation.  

Twice the amount of oxygen doubles the current. In order to measure the current we measure the voltage over the potentiometer. Ohm's Law tells that R=V/I and because, after calibration, the resistance doesn't change anymore, V/I remains constant. In other words: when current I increases, voltage V increases proportionally.

Nota bene:

a  The electrode uses oxygen and has to be moved (or the water) in order to keep the diffusion through the membrane at a constant rate. 
b  Diffusion is an extremely temperature sensitive process, which makes calibrating and measuring at the same temperature imperative!
c  Reducing oxygen at the Ag-pole causes Pb to be oxidised at the lead-pole. Lead-ions combine with hydroxide-ions to form a gray layer of lead hydroxide, resulting in a decrease of the Pb-area: the electrode declines. The longevity of a freshly prepared electrode can be enlarged by storing the electrode in a jar with 1% Na2SO3-solution, everytime the electrode is not used.
After a few days an electrode will become useless, and the Pb-surface needs to be polished with a soft abrasive and the electrode has to be prepared again. If you want to know everything about the properties of oxygen electrodes, then click on the site next door.