It's like a very minimal version of ActivityPub. It takes an hour to go through the whole spec and addenda.
Then Jack Dorsey got interested, gave the project a big grant (in BTC), and a lot of crypto hype flew into it. But while it is a convenient excuse to say "crypto, therefore bad", the protocol is itself completely unrelated and IMO quite neat. There is a lot of potential for systems that anyone can comprehend in their totality in an afternoon.
A Nostr account is identified by a public key, you follow accounts by following public keys and the ability to post as an account is controlled by the corresponding private key.
This tool lets you broadcast your pub key on twitter using a specified format, and the app will add you to the directory, and you can use it to find others that have also done that.
Also, if you go to https://snort.social/new, you can enter your twitter handle, and it will find everyone from you're twitter follows that you're not already following and let you sign up to follow them all.
It looks great, works well, the code well-written and super easy to hack on.
It seems to work a little differently to other clients by aggregating all the content on one relay first before sending it to the client, but I prefer this as it is faster and uses less bandwidth.
Fiatjaf who often posts here also stated that he would like to nostr to be used by non bitcoiners and even people who are antagonistic to bitcoin.
Update: It seems to be partly a twitter alternative perhaps using lightning network in some way. I set up an account on astral.ninja, created keys, username, saw that there were relays that were defined already. I couldn't see any posts in my feed, and when I tried to make a post it just hung and never posted anything. Suffice to say my initial experience started off okay, then dissapointment.