Could anyone perhaps tell me what this is?

Cold start injector electrical connection.
First find out if wires are touching (bare wire to bare wire), tape bare spots then do the following.

Easier way to see if cold start injector is working. Unbolt injector put in a plastic bottle(cut the top off a small Coke bottle) and try to turn the car over. if it is working it'll put fuel in the bottle. lay towels down so it catches the fuel spill.

Without the key in the on position, no juice to it. Key in on position it should have juice to it, or at it will when cranking. Cold start valve is initiated when starting cold, (20-30 seconds), and also from a hot start ( 5-10 seconds) if working properly. Long enough to put fuel into the bottle.

Test light on poles should light a test light when engaged. Alligator clips onto power and ground in switch will tell you if you have power. test lights are your friend.

here is a good article about the injector.

Hot Start Problem Fix

I would still remove the injector and do the bottle trick since it seems like you have fire to the plug. I would not run the car without the injector.

Does your car not run at all? Do you have spark?