The three cables are
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- **Always-hot** and **neutral** from the service/supply panel
- **Always-hot** and **neutral** onward to other appliances
- **Switched-hot** and **neutral** to the lamp

(and we're ignoring equipment safety ground, because in mains electrical, it's a safety shield only.  It's not a player in any capacity, *electrically*, until there is current leakage, in which case it provides a safety shield. The hot-neutral supply is wired the same as an isolated system, with no concept of "chassis ground" like you might find in a car. There is no equivalent in low voltage electronics.) 

I am no fool, but I often need to work on panels some years later. As such, I am a huge fan of using tape or shrink-tube to re-mark hot wires based on their function.  Keep in mind you can't re-mark amongst hots, neutrals and grounds, except white/gray (neutral) wires to be a hot, if it's in a cable.   It works out nicely as a convention to use red (blue or yellow as alternates) for switched-hot. And I'm famous for double-yellows for 3-way travelers - they go on the brass screws after all. 

So I would mark the switched-hot wires with red tape. 

Here's an electronics question for you.  
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*I'm going to say Vss instead of GND because in mains electrical, Ground is actually something else.*  

You have 5 volt Vcc (+) and Vss (-) going into a circuit.  The Vss specifically comes from the power supply on a black wire, then goes three ways: to the Arduino controlling it, to the solid state relay, and to the lighting LEDs controlled by the relay.  

You want to add an indicator LED to show when the Arduino has access to DC supply. You connect from Vcc through a resistor and the LED to Vss. However, there are four Vss wires.  **Which one do you use? The one to the power supply? The one to the Arduino? The one to the relay? Or the one to the lighting LED?**

That's a trick question, of course; all four are already connected, and they need to stay connected. The additional Vss wire would be added to the group.  

So it is with mains neutral.  Neutral is analogous to Vss.