It's basically just a nice way of composing the different parts of your system.
E.g. you could write a NixOS module to manage your web app. You declaratively
configure that you want to run Nginx, Postgres, etc. open some ports, connect to your VPN and basically everything else you might want. There are a lot of existing modules, so in most cases you have to write very little code yourself. If you want to scale your system to run on multiple systems or containers, you can do that with relative ease.
You also have a singular source of truth for all of your information, down to your application binaries. Your configuration says you are using Postgres version X.Y.Z with compilation options A, B and C, so that's exactly what is running on your systems.
E.g. you could write a NixOS module to manage your web app. You declaratively configure that you want to run Nginx, Postgres, etc. open some ports, connect to your VPN and basically everything else you might want. There are a lot of existing modules, so in most cases you have to write very little code yourself. If you want to scale your system to run on multiple systems or containers, you can do that with relative ease.
You also have a singular source of truth for all of your information, down to your application binaries. Your configuration says you are using Postgres version X.Y.Z with compilation options A, B and C, so that's exactly what is running on your systems.