"Reporting" creates a kind 1984 note with tags to reference the npub being reported, and the event you are reporting them for, when applicable. Depending on the client, you may have the opportunity to include additional context.

What happens when you report someone? Probably nothing. There is nothing in the Nostr spec (defined in NIP-56) that requires anything be done by any relay or client as a result of you reporting someone.

It seems that most clients will automatically add whoever you reported to your mute list, under the assumption that you wouldn't want to see anything more from them if you felt it necessary to report them.

There are a couple suggestions of what clients and relays COULD choose to do with those reports, though.

On the client side, they could choose to hide posts from npubs that have been reported by users you follow. Amethyst, for instance, has opted to take this approach. If a note has been hidden due to reports from your follows, there will be a message stating it has been hidden for that reason, and you have the option to view it anyway.

On the relay side, NIP-56 discourages relay owners from automatically removing content that has been reported, since that can easily be gamed, but does suggest that the relay could flag certain npubs as "trusted moderators" and act on any reports that come from them.

I don't know of any relay implementations that have any means of reviewing and acting on received kind 1984 notes, though.