It is a chassis ground strap. It electrically bonds the case of the radio to the body of the vehicle. It reduces the posibility of static electricity damage and electromagnetic interference from other electronics in the car. It is a good idea to connect it. It also helps improve radio reception because it part of the antenna system.
If your supply is cut for a couple of seconds, then you will need quite a large capacitor to keep power supplied to the head unit, especially if the volume is turned up quite high at the time.
You will also need to think about the choice of diode that will be able to cope with the current demands of the head unit and also the inrush current of initially ...
What you have there is part of a "Harness interface". It's for aftermarket stereos for newer vehicles that use a "data bus system" or a instead of a red ignition switch (acc) wire. You're missing the door chime part to complete the set. Without it idk how you're gonna bypass or get it to work. I found your post, albeit almost a year later,...
Solar Mike's answer is correct in it's description, however I would also add the following from experience.
When I have done this in the past (20-odd years ago I think!) the harness adaptor came wired with the correct colours and pin layout according to the ISO specification and the majority of cars but if I remember correctly the permanent and switched (ACC)...
I would put the switch in the power supply (+) wire.
But if there are two power wires I would not switch the one controlling the memory settings, but that would leave an albeit small energy drain.
Make sure you also fit suitable fuses.
Just put a switch in the red lead.
Even an inline table lamp switch would suffice, the voltage is low and so is the current.
Or you could get a small on/off round button type switch and mount it neatly in a bracket.