I am not sure, but in Nix I declare the desired state of installed packages and configurations in an obscure language and the package manger takes care of that, right?

The package manager is only one (very important) component of the system that applies your configuration, but otherwise this is a good description, yeah.

Now the module declare reasonable default configurations? Like http server starts on system start and serves on port 80?

Obviously, it depends on each individual module, but so far, I’ve mostly been fine with the defaults. Typically, it doesn’t modify the configuration, unless you explicitly specify a configuration value, therefore using the defaults that the software normally uses.

Now you lost me at the Home-Manger. I can declare stuff in my home folder. OK, so for user-wide configuration? For packages and configuration in the user space? Or what?

It’s for user-wide configuration, so what would generally be stored in dotfiles. For example, you can configure the search engines in Firefox. Or the panel layout in KDE.

Home-Manager can also install packages, which is useful, because it can also be used standalone on other distributions. And in particular, you usually want to declare that a package should be installed and what user configuration it should use, all in one place…