Google searches have only yielded 5th grade level examples (“the modem talks between your ISP and your home network!”) or articles I would need a degree to understand. Can anyone provide an explanation that’s somewhere in between the two? I understand the fundamentals of how the Internet works, and how LAN works regarding a router and individual devices, but I’m curious to know more about the link between those.
As others have noted a modem is a modulator / demodulator.
Most modems are designed into other things. Like cable coax modem/router/switch/wi-fi access point. Or other things. Or in a cell phone it converts bits internal to the phone into radio signals or back the other way. Many things people call a modem is really a more complicated box with a modem built into it.
In the basic definition of the term it is bits <-> analog wave forms. Back in the day it was land line modems and the wave forms could be heard by most people if they listened “in”. Actual FAX machines (not email pretending to be a FAX) still do this. Connected to the “bits” side of a modem is usually a circuit that takes those bits and organizes them in agreement with the other end of the connection. Mostly these days Ethernet.
Most Fiber setups do NOT have a modem as they have networking bits already in the light in the fiber. They do “media conversion” between fiber and copper.
And if you want to dig deeper look into how DSP (Digital Signal Processing) works, Fourier Transforms, and how Wi-Fi radios encode things, and so on.