My feeble attempts to understand tell me that they look like RCA cables, but they only have one wire... is that right?
If there's only "one wire" then you can't complete the circuit. Each cable needs at least two wires, one + and one -/GND, and you need two cables - one for Left and one for Right. So overall you need four wires, two in each cable, running L+, L-, R-, R+.
If you mean one cable then that can't complete a circuit either, since one cable with two wires will only do one analogue channel.
The only application for one cable with two wires in it is for a coaxial SPDIF connection, and these typically would not be labeled "preamp jumper" since they're not connected to an analogue connection from a preamp to an amp, but between a digital source and a DAC, DAC-HPamp, or receiver.
My brain can just not resolve what that accomplishes. I understand how it is used on an amp with pre-out/main-in but I cannot compute why one wire in each actually does what they do.
"Main In" does not mean anything like "Primary (or Primarily) used input." It means "Direct into main
amplifier circuit that bypasses the preamp circuit." Most integrated amplifiers have the two circuits on the same board or at least internally wired. A few have this connection outside of the amplifier to facilitate using the integrated amp as either amp only or preamp only. For example, you can get a tube preamp and hook it up directly to the amp circuit via the "Main In," or if you just need more power when you upgraded to tower speakers but don't need any tube coloration, you can just get a more powerful pure power amp to hook up the Pre(amp) Out(put) of the integrated amp to control it.
For example, you start with a NAD 304 and a Focal Chorus 706. You think it's too bright, but you can't use EQ and also don't need more power. You might want to add a better headphone amp for an HD6xx too. So you put a Little Dot MkII between your CDP and the Main In on the NAD 304. You get a tube headphone amp and use its tube preamp to roll off a bit of the highs on the Focal speakers.
Alternately, maybe you upgraded the Focal 706 to an Aria 948 because, as much as you can drive the 706 loud in a large room, the bass response still trails off when you sit 2.5m away with the speakers 2m apart. You don't have a problem with the coloration of the NAD 304 preamp (since the sound on the 706 is otherwise OK at 1.25m away with the speakers 1m apart, but the soundstage is also too small), but you need a more powerful amp to 1) deliver enough current to drive the two additional 8in woofers and 2) to still hit 85dB with no problems from 2.5m away. So you went off and picked up a NAD 2400PE and hooked it up to the Pre(amp) Out(put) of the NAD 304.
Now...if that's what those sockets are primarily for...what are the jumper cables for? Because those amps typically come with just a metal bar cast to a shape that makes for a convenient package (small and won't break while the amp gets tossed around until it gets to your house). It isn't pure copper, and adding more metal than just copper doesn't mean you get the same conductivity. Some can be pure copper or brass, but then that gets exposed to oxidation (my second NAD 304 in another part of the house started going green after a few months) and possibly corrosion. Some can be coated in thicker brass or stainless steel to prevent corrosion, but that's still highly susceptible to electronic noise, something that wasn't as big of a problem decades ago when mobile phones were something in cars or bulky military grade satellite phones. Or maybe you just want a subwoofer too.
I replaced the jumper metal with a pair of custom Y-jumper cables cut from the some Belden bulk cables (you can buy them in 1m increments here). Made 0.3m cables to connect my CDP to the CD input on the NAD 304, made a Y-cable using one larger pair of RCA sockets and had a short run come out of it with a female RCA plug, and a slightly longer run with a male RCA plug. Large male plug went into Pre Out, regular size male plug went into Main In. Then I made two 2m runs with male plugs on both ends to go from the Pre Out split female plugs to the subwoofer's stereo input. Sub sat on a platform to raise it and reduce timing variance and reflection timing, allowing me to cut them higher (100hz) while sitting in the center of the two Wharfedale Pi10 speakers (gain on sub was low). Preamp on the NAD 304 controls both its amp section driving the Pi10 and feeding the Wharfedale 10in sub.
And then coincidentally the next time I was checking something in the back of the equipment my phone which I have been using as a flashlight (not an app - it's one of those old Nokias with a flashlight bulb on the back) and noticed it wasn't causing any interference any more.
