Electronic oxygen concentration sensor
I cannot say as to your specific sensor, but most oxygen sensors are electrochemical sensors built around concentration cells.

Take a look at the following diagram of a simple zirconia-based oxygen probe from Wikipedia. This type of sensor is very like the one in automobiles.



In the middle of the sensor is a gas permeable zirconia $(\ce{ZrO2})$ membrane between two gas permeable electrodes. The membrane and electrodes form the electrochemical cell. In many cases, an electrochemical cell will use a reference electrode with a standard reaction going on for comparison. In this sensor, the standard reaction is the same one that is going on at the other electrode. The difference is that at the standard electrode, the partial pressure ("concentration") of oxygen is known and at the other electrode it is unknown. 


  But wait, how does that work? 


Let's take a generic electrochemical process, where $\ce{M}$ in the following equation represents something generic that we can oxidize:

$$\ce{M(s) + O2(g) -&gt; MO2(s)}$$

This cell has a standard potential $E^\circ$. The actual measured potential, however, will depend on the partial pressure of oxygen $P_{\ce{O2}}$ because the standard potential is defined at $P_{\ce{O2}} = 1\ \text{atm}$. The relationship that gives us the actual electrode potential at some other oxygen level is the Nernst equation;

$$E=E^\circ - \frac{RT}{nF}\ln{Q}$$

Where:


$R$ is the ideal gas constant
$T$ is the temperature 
$n$ is the number of electrons transferred (4 in my example)
$F$ is the Faraday constant
$Q$ is the reaction quotient, in this case $Q=\frac{1}{P_{\ce{O2}}}$


If $P_{\ce{O2}}$ is large, then $E$ is small and vice versa.

Now, we have two electrodes, our unknown and our reference, each with their own potential:

$$E_{ref}=E^\circ - \frac{RT}{nF}\ln{\frac{1}{P_{\ce{O2},ref}}}$$
$$E_{unk}=E^\circ - \frac{RT}{nF}\ln{\frac{1}{P_{\ce{O2},unk}}}$$

The voltmeter in the device measures the difference between these two potentials and does some maths to calculate back $P_{\ce{O2},unk}$ and then convert it to concentration or percent. Note that it does not even matter what $\ce{M}$ and $\ce{MO2}$ were, since they are not in the equation and even $E^\circ$ cancels out. 

$$E_{unk}-E_{ref} = \frac{RT}{nF}\ln{\frac{P_{\ce{O2},ref}}{P_{\ce{O2},unk}}}$$


  What substance might this have been? 


If your sensor was this kind of sensor, the crusty mess is probably zirconia.