In case a relay was offline, or maybe you were offline, or for whatever reason, if your note did not reach a relay you wanted it to, then you can force a rebroadcast to all of your relays with this button.

Another scenario is that you see a post that you like and you just want to help it reach. Reposting is OKAY, but it just signs a note that you "approve of" another note. It doesn't physically help the note reach.

In some cases, you might see a quote post for example but the embedded note is unreachable. By rebroadcasting, you take a note that you have received from maybe 1 relay, and push it forward to all of your other relays.

It helps people searching hashtags and global feeds see the note mostly, but if you engage with it, it also helps your followers too.