Nostr: What is a Nostr relay?

Short answer

A relay is a server that receives events from clients and answers event queries. It can choose what to accept, store, and return, so relays are not interchangeable copies of one guaranteed global database. Public, paid, private, and community-oriented relays can have different rules. Your client may connect to several, and your relay choices affect who can discover your posts.

Sources

NIP-01: Basic protocol, NIP-11: Relay metadata.