It's kinda like Bitcoin, but it's not on the actual Bitcoin blockchain.

The public key and a "digital signature" are sent over the wire with every note, like, repost, etc. (collectively called "events") you make on Nostr. The events are stored on the relay servers.

(OK, if that's enough for you, you can stop reading here. To learn more about the signature, read on.)

The signature is made with your private key and the message. Anyone who has the public key and signature can, through some math calculations, verify that they match. That's how the network knows it's you.

If I wanted to impersonate you, I would need to craft a digital signature that matches your public key. This is *nearly impossible to do* without the private key; I would need to basically try random signatures over and over again for years.

For more info, there's a great Computerphile video.