TVS DIODE: Min breakdown voltage and Stand off voltage
The minimum breakdown voltage is the voltage at which the TVS will conduct the specified amount of current listed in the datasheet. It's not a hard clamp at this point, but the device is close to or at the 'knee' in its reverse breakdown curve and will fully break down if the voltage continues to increase. (The hard-clamp voltage is usually specified separately, and is sometimes referred to as \$V_C\$)

The stand-off voltage is the highest guaranteed voltage at which the TVS will not conduct appreciable current. It will conduct some small leakage current, but will not break down and clamp.

It's obvious once the definitions are understood why the breakdown voltage must be higher than the stand-off voltage.