I think the usual answer is 'reproducible builds' -- you can basically set up your computer, its software, and all the software settings - with a single configuration.nix file. The hardware configuration is created at build time, so you can move to a different machine and have the exact same software all set up. If you're managing a bunch of boxes then you can push upgrades and fixes to them and they're all done. Imagine capturing all your software, and their configurations, in a git repository - did something break? Switch back to the last "version."

The other great benefit is that often, especially in FOSS/linux scenarios, package dependencies get broken or are conflicting - e.g., Favorite Software A is dependent on release 1.2.1 of something but Favorite Software B is only compatible with release 1.3.4 of that same dependency. You can pin dependencies and avoid conflicts.

Others who are far more tech-savvy can correct or enhance the above, but that's my take on it. I'm a bit of a command-line geek, love to play with new software and learn more linux tricks etc., so it's more of a hobby thing for me. You can install it and have a UI similar to gnome but the real benefit is building up your configuration and making use of that.