It doesn’t really verify anything, but it makes your account easier to find. It’s called NIP-05.
You can read all about it here: https://nostr.how/en/guides/get-verified
Discussion
Yes, there was a lengthy discussion about that. nostr:npub18ams6ewn5aj2n3wt2qawzglx9mr4nzksxhvrdc4gzrecw7n5tvjqctp424 is correct in referring to it as a nostr address because it's simply a domain associated with the user's profile.
Thanks!