Ok, heres my run down:

Nix is a package manager with the goal of making it so that when you install a package at a version, you always get the same thing.

But isn't that how all package managers work? Not at all. Most software requires other software to work (dependancies). Those dependencies also have dependencies, and so on. If a version of the dependency changes between installs, your package works differently. So Nix forces the package to specify what version of the dependency to use.

But version numbers are pretty wishy-washy, so nix actually requires git commits. This is good, since it turns out, the compiler and libraries used to build the software are dependencies, too. Building with a different compiler can change the way the package works. So Nix forces the package to specify how to build it also.

So Nix is a package manager where each version of a package is built against a known compiler, and comes bundled with a known set of dependencies.

This allows some cool things, like generations. Change your list of installed packages (or configuratian, it handles that too), nix can save the old config and instantly go back to it. No more bricked linux install (if it can get past the bootloader). Also lets you do os-level per-directory installs. Have two projects that each need a different version of c compiler or postgres? Nix makes that easy. Want to make sure all dev machines in your project have the same python version? Just check in the config.

The Nix / NixOS documentation is notoriously bad and that sentence is a prime example.

My advice, you can probably get on quicker with YouTube than with the official documentation. Or you can just muddle through like I did. Might take you longer though.

I'll take a shot at unpacking the functional part though: Imagine a system like a math equation, like "solve for x". The system is the result of that equation. You define a couple of constants, like "I want it to run KDE" and nix will try to fill in the variables, eg. to run KDE you need bash, python, Wayland, etc. Like in school, you can break this equation down further, eg. to solve for Wayland, you need wlroot, mesa, some libs, etc. In the end, nix will solve your equation to a system that has everything that you want. Not only packages, also systemd units, your whole /etc and so on.

It's of course much simpler to imagine it like this. NixOS essentially builds your system from the ground up using a configuration file instead of by running a bunch of commands. Each configuration change produces a new system in the same sense that 4 = x + 3 solves differently than 5 = x + 3. The essential part is that Nix always solves the equation forward, if you will. So where apt-get install foo-service would put a line into /etc/groups, changing the file in place, Nix would replace the whole file because it knows what the file has to look like at all times given the configuration. Further more, it keeps the old configurations around. So if you liked your system better solving for 4 than for 5, you can just go back. Since Nix knows exactly how the system needs to look for 4, there is no "mess" because it does not need to remove things. It always builds forward.

Hope that makes some sense :D

Ooof, that word though.