It's just like mail. An inbox is notes for you, you receive notes on those relays. An outbox is where people can find your notes, you publish your notes on those relays.
If I want your notes, I use the relays you have set to communicate with you. You do the same on your end, using my relays to communicate with me.
It makes it so people don't need common relays, making Nostr more decentralized.