It doesn’t iterate on Flatpak, it’s its own thing.

Describing Nix in detail would require a PHD thesis but in short it takes the concept of a version to the extreme; capturing every property about some package and encoding that into the “version”; a package bar-0.1.0 that depends on foo-1.0.0 and a package bar-0.1.0 depending on foo-1.0.0 that has been built with the same GCC but a patch applied to it are considered entirely separate. This implies that your package bar cannot accidentally depend on the wrong foo and that both can be present at the same time.
Using a functional DSL, you implicitly build up a tree of such “exact versions” of dependencies and this tree is then “realised” bottom to top.
It takes many inspirations from functional programming such as purity and immutability. The build takes place in a sandbox with no filesystem access outside the declared dependencies and not networking whatsoever and cannot be changed after the fact. This aims to ensure that a build really only depends on the paths it claims to depend on (those paths must also be “exact” versions) such that running the build again with the same inputs results in the exact same output.

Again, describing Nix in detail would go beyond the scope of this comment but this approach comes with many useful properties which prevent entire classes of issues you could encounter with classical package managers such as dependency hell.

It’s not tied to NixOS either (that’s its own thing again; doing Linux system configuration management using Nix), you can install Nix packages on pretty much any Linux as it doesn’t interfere with your classical package manager. Give it a try: https://nixos.org/download.html