"Report" does what it says, report the phone number as spam to Google. This will help users of Google's caller ID (e.g. Nexus device users) in the future, since number reported as spam will be shown as "Suspected spam caller" or "Spam" as caller ID.
From Nexus official support,
Mark calls as spam
You can mark all calls from a number as spam to keep from getting any more and report the spammer.
If you see "Suspected spam caller" or "Spam" as the caller ID, the call might be spam. You can answer the call, or block and report the number.
I normally file call complaints with FTC Do Not Call Registry. Does Report do this for me?
I believe no, because DNC is country-dependent (e.g. FTC's National DNC Registry in US), and I've never heard Google working together with these kinds of government instance.