I tried Nostr some time ago, but I didn't stick much long. As far as I'm able to tell, there are lots of functionality, but there's a very serious downside: its userbase, mostly comprised of "anarcho"-capitalists, cryptobros, anti-vaxxers and climate change denialists (and literal flat-Earthers), misogynists, white supremacists, etc... but they swear they don't like the orange turd, but they share the same... erm... "moral values"; it's the so-called "alt-right", ergo, Nostr is mostly a nazi bar. Hence why I didn't stick. Oh, and there's a lot of spamming from bots, as well as the so-called "agentic AIs" (OpenClaw) posting as they farm Bitcoin (more on the latter later).
If it weren't for the toxic userbase, the technical features are surely interesting.
In a nutshell, relays are to Nostr as instances are to the Fediverse, except one has to use apps (e.g. Amethyst) as the front-end, as relays won't necessarily provide a full-fledged Web UI like Fediverse instances do. Unsurprisingly (given how it's mostly comprised of cryptobros) it got a native support to Bitcoin "lightning transactions" (one can "zap" a Nostr event, i.e. proceed with a microtransaction transferring Satoshis to the author of the Nostr event). Also unsurprisingly, most relays are paid ("something something no free lunch").
Relays and apps may or may not implement certain NIPs (Nostr Implementation Protocol? I'm writing from memory so I'm not sure of the acronym). E.g. there's a NIP for long-form content (blogging), a NIP for videos, a NIP for marketplace (akin to craigslist/Facebook Marketplace), a NIP for communities (akin to Lemmy communities), etc... Think of NIPs as plug-ins rather than things imbued into the platform, which (differently from the Fediverse) allows for adding features without having all relays and apps to implement the same features. Every event has one or more NIPs, and it's up to the relay to accept or refuse it depending on which NIPs the relay is configured to allow, and it's up to the app to display a given event depending on which NIPs the app implements.
In this sense, DMs are also a NIP, and I guess there are more than one kind of DM system. There are certain implementations using the notes NIP (iirc it's NIP 01, the most basic kind of event and mostly supported across relays and apps) to transmit base64-encoded payloads of some kind of E2EE message, and it's so poorly implemented that it spams the global feed.
Nostr relays can be self-hosted just like Fediverse instances, but one can use multiple relays simultaneously in order to get a broader reach (think of having alt-accounts across different Fediverse instances and crossposting, except all alt-accounts have the exact same handle and ID because Nostr handles are Nostr-global nprofile123abcdef... addresses).
There's more to it, but my reply is already lengthy, so you can AMA if something isn't covered by the afore explanations as I did use Nostr (and ended up not staying due to its userbase, but used it nevertheless so I got some hands-on experience).