Twitter verification is meant for people with sufficient notoriety (say, elected officials, artists/actors, leaders in their field) to prevent impersonation and fraud.

So, if I get rickrolled on twitter, I can tell whether it was a post by the real Rick Astley or by some impersonator.

Or for another more topical example, the tag #TrumpIsDead is currently trending on Twitter. If I click on that for more information, the verified check might tell me who has notoriety as a journalist or which accounts represent official news organizations, vs who is trying to further promote a false meme (in protest for Elon forbidding content moderation in the lead-up to the US elections)