Aurora is on version 1.9.5 C#, available at the Aurora Forums.
Contact Erik on the forum for a wiki account.
(This is from an old forum post by Steve. Transponders do not currently play any role in Aurora.)
Transponders are a way for a ship to identify itself to other Empires if it wishes to do so. When a ship is built or refitted, the transponder will automatically be set to the class of the ship and the status will be inactive. Each ship can change it's transponder to any class of that race or to any alien class for which you have learned the transponder codes. You can activate/deactivate the transponder and set its class on the Ship window and there are also new Activate and Deactivate Transponder fleet orders.
Transponders could also be used for IFF in the case of future minefields or fire and forget missiles.
Another possible use would be two or more Empires creating a treaty which made transponders mandatory in certain systems, Obviously there are a lot of deception possibilities around transponders.
The actual mechanics: turning on the transponder shows your position and transponder code to any other ships or pops in the same system. That is the extent of the information though. An alien race would still have to bring you within sensor range to get any confirmation of what you are telling them.
A standalone transponder signal will be represented on the map as an icon with an associated transponder ID. If you also have a sensor contact for the same ship, the Transponder information would be included in the contact data instead. It'll automatically add any alien transponder codes to the Tac Intelligence window if your sensors match up a active sensor contact with a transponder. It'll also allow you to associate an ID with a known alien class on the Tac Intelligence window so that in future transponder IDs for that class will be shown by the alien class name instead.