https://joinjabber.org gives a good introduction. Just with the difference that you don't need to register an account because you already have one here on SLRPNK which also works with XMPP clients.
XMPP
XMPP (aka Jabber) is the community-owned standard for real-time federated messaging.
JoinJabber.org admin support chat
So is that what is meant when people say slrpnk is "integrated" with xmpp, that we can use our slrpnk credentials to log on xmpp clients?
Is there any feature crossover from the integration like being able to reply to posts on lemmy using xmpp or just the shared login?
For now just shared logins.
Its basically federated WhatsApp, in fact WhatsApp uses a slightly modified XMPP under the hood.
You can compare it with e-mail ... in a way.
You can set up a server, you can register on an existing server, and you can communicate with everyone else, regardless what server they use. You can send long text, you can send short text, or media. But not as asynchronous mails but as chat messages like in any other common messenger service.
Like with e-mail you're not limited to a specific app or a specific website or software. You don't need to give someone your phone number, or do weird authentication things. You can have REAL end-to-end encryption, too. Most clients support that.
‘chat thingy’ I use are messenger apps (is that even the same?)
Almost. XMPP is a protocol, and a "messenger app" would be an XMPP client, for instance Conversations. All your messenger apps use some protocol. Most of them use a proprietary protocol meant to be used inside the app's "walled garden". XMPP being an open protocol, it's meant to be used by different clients.
Why is XMPP relevant to solarpunk? XMPP is quite old and thus, very resource-efficient. However, the X in it stands for extensibility, meaning that you can also do "modern chat stuff" with it.