Nostr: How do Nostr clients and relays work together?

Short answer

A client signs an event with your key and sends it to one or more relays. Other clients ask relays for events matching filters, then verify signatures and display the results. Relays may accept, reject, retain, or remove events according to their rules. Connecting to several appropriate relays improves discoverability, but it does not guarantee every reader will see every post.

Sources

NIP-01: Basic protocol, NIP-65: Relay lists.