In a sentence, Nettle is a system for synchronizing data and proving it has been created by its real authors.
In more than one sentence, Nettle is an alternative (but not replacement) for other decentralized systems, such as blockchains, which can be very wasteful if not used effectively. Proof-of-work consumes a lot of power and ultimately becomes centralized when/if only people and groups with lots of purchasing power can obtain hardware, which I think is quite likely — even today — given the prices of mining hardware. Proof-of-stake is also centralizable because the coins needed to stake effectively cost a lot of real world money too. It's simply not effective for your average Joe to start staking or mining and help out in securing a network against people with less benevolent intentions.
The Nettle specification and reference software is very bare, running only two thousand lines (at least when I last checked). Right now, I'm rewriting it in Common Lisp, which will probably compact and refine it further. A Nettle server only needs to track the current state of the files it maintains, and some basic metadata about it. This metadata is just its name, signature, owner(s) and "parent" entities the Nettle daemon uses to decide what rules to apply to the file. Nettle handles key management and a rule engine for the user.
The Nettle reference software also uses a license formulated for new software projects which don't need commercial backing called the Cooperative Software License. We think that if software is like science, and if early experiments and commercialization end badly, we should try to keep our experiments as public and community-friendly as possible. I've been working on this project for about 6 months now, and I don't think it's close to being ready. There's a lot that could go wrong, such as exploits in our methods of signing things and getting the current state from other servers, and it'd be a letdown for anyone involved if a commercial project were to flop because of that.
Pessimism aside, I'd love if anyone could help contribute to the Lisp port, host servers such as this one, or contribute to a web client, which hasn't been started yet. I think this project is a very nice alternative to other decentralization methods, and can help power other new ideas which could be otherwise very expensive to set up.