As it is difficult to determine exatly how the batteries are charged from the alternator it is not possible to be totally certain what would be the best way to proceed. If there is a double (diode bridge) output alternator or some other existing battery disconnect system then diodes later may not be needed as the head unit could connect to the Aux battery all the time and if this runs flat you would have to start the engine to charge it and this may automatically connect the two batteries already.
If you want to operate it from the main battery with engine not running you couldconnect the ACC line to control a relay that will supply Main power (NO) to the head unit (COM) when the ignition is on and then feed from the Aux battery (NC) when the ignition is off. You will have a power glitch when you cycle the ignition.
If the batteries are connected together at the alternator then none of the extra stuff afterwards realy matters as both will drain together.
You can have a look at the large selection of solutions that have been invented for your situation in the list of pictures blow. There are smart products and DIY solutions, some of those solutions will not work and you can ask here if you want to confirm a specific case. The important thing is to establish how the two batteries are currently separated from each other at the moment when not charging and if the second battery would be nice to have available for starting if you let the main battery run flat with the headlights illuminating your campsight.
Some of these are intended for high currents and others for slower charging only. Some will sense the main battery voltage and only hook up the other if the main battery if mostly charged.
Looking at figure two, the polarity has been marked such that, if you hooked it up to a battery like that, current would flow.
In figure one, the diode is reverse biased by the power supply, and current will not flow.
If you unplug the power supply, the solenoid drops out because the current stops flowing through the coil. However, the coil has inductance, which has the property of resisting any change in current flow - that is, the power supply will stop producing current, and the coil will start producing current in the same direction, until its magnetic field is totally gone.
Think of the stripe as an arrow showing you which way current is allowed to flow through it, and imagine you just unplugged the power supply. Understanding that current will no longer go through the power supply, you should be able to see that it will now flow out of the coil and through the diode.
If that diode were not installed, the coil can produce something called inductive kick, which can and will destroy the power supply by pushing voltage higher until it gets current flow - possibly through something that shouldn't be passing current.
The diodes are there so that there can be two separate mechanisms for enabling the main headlight relay without interfering with each other. From the labels on the right, it looks like the two mechanisms are the normal headlight switch, and the momentary passing switch, which makes sense. You want each to be able to turn on the headlights independently.
You now say you are looking for more of a low level electrical explanation of what the diodes do instead of the high level conceptual explanation you originally asked for.
The diodes allow either switch to turn on the relay, but still remain independent. Presumably at least one of the switch lines is used elsewhere in a way that it shouldn't be signalled when the other switch is activated. Without the diodes, there would be only a single switch line, and that would be activated identically by either switch, making it impossible for other parts of the system to determine which user action caused the headlights to turn on.
For example, the general headlight switch may also turn on some running lights or maybe a indicator on the dash that the passing switch is not supposed to turn on. With the diodes in there, the general headlight switch line remains unasserted when the passing switch is activated. Each switch can activate the relay, but there is no connected between the switches.