Relays are usually small black cubes with, commonly, 5 pin connections. The function of a relay is that of an electrical switch, opened and closed by an electromagnet. Your dash switch supplies power at low amperage for the electromagnet, which in turn closes the main high-amp switch. This puts the hard work inside the relay where the contacts are large and rated to do heavy work, and leaves the dash switch to handle only the small amperage needed to run the magnet. Trying to run 30 amps through a dash switch has lots of down-sides, not the least of which is running 30 amps or more inside the cabin and behind the dash where you can't get to it if it catches fire.
Two of the connections on the relay are for power and ground for the switching circuit from the dash switch (these activate the magnet and close the switched circuit), and two are for power in/power out to whatever you are trying to run, such as your lights. If provided with a 5th pin, that one is power out opposite of the switched power out. That is, the 5th pin is constant hot when the magnet is not powered, and goes dead in favor of the other power out when the magnet is active. Like a diverter switch. Power will be available to either one or the other power out, but not both at the same time. I have yet to come up with real a use for the 5th pin, so I blank off the wire on the harness. The 5th wire would allow you a work-around on the relay in the event of relay or switch failure because it is constantly hot, so in the event of a failure, you could swap the non-working switched power out for the constant hot power out, and power your lights or fan or whatever, but I wouldn't worry about it for now.
So, think of a relay as a remote controlled switch.
Side note: I would use one relay per pair of lights, but would not use a relay to fire up the other two relays. Instead, I would run the switch wire from the dash to both relays and let them share the same source, just as I would allow the two relays to share the same high-amp power source. The amp draw on a relay magnet is low and running two relays on the same switch won't overload the switch. Using two or more relays in series will work, but makes diagnostics a pain if something goes wrong. It is more complicated than it needs to be. So I would not use a relay to trigger other relays.