The breakdown voltage is the point at which a diode begins to conduct electricity. Below the breakdown voltage, no current can flow. I believe the typical breakdown voltage on a silicon rectifier diode is about 0.5 volt. Note that a diode has not only a forward breakdown voltage, but a reverse breakdown voltage as well, after which current will be allowed to flow backwards. On a zener diode, the reverse breakdown voltage point is quite useful, as it can be used in a clamp or voltage reference. On a rectifier diode, you must avoid having a reverse voltage present across the diode that exceeds the reverse breakdown voltage, or the diode will be converted into a friode.