perhaps that you can reverse the anode and cathode with no ill effect, or that it can take valid measurements both increasing and decreasing from its rest state (eg. pressure sensor could measure expansion or negative force).
Are you sure the OP isn't talking about transducers that go both ways? A speaker is also a microphone, an antenna can convert an RF signal into electricity, and RF electricity into RF. There are many cases a transducer swings both ways.
After Googling irreversible sensors, I believe that a reversible sensor changes state when the relevant stimulus is sensed, and changes back when the stimulus is removed. In contrast, an irreversible sensor continues to indicate that the stimulus has occurred, even when the stimulus is removed.