For most clients, they just list your relays as read (inbox), write (outbox) or read/write (inbox and outbox).

Now, we've always had the ability to set which relays we read from and which we write to in our Nostr clients. But the outbox model adds a bit of functionality to these choices. Without the outbox model, you have to set read relays that your follows are writing to, or else you won't see their notes and replies, and you have to write to relays they are reading from, or you won't see theirs. That has a centralizing effect over time, and discourages the use of smaller relays.

On Nostr clients that support the outbox model, your inbox relays aren't the only ones you read from. Rather, they are where other users should expect that you will see a reply, reaction, or zap, and clients should write notes that mention you to those relays. Meanwhile, outbox relays are where you are writing to, and Nostr clients trying to find and display your notes should be fetching them from those relays. That way a user who follows you might have a completely different set of relays that they are reading from by default, but they will still see your notes, because their client is fetching them from your outbox relays.