If the account belongs to an official invite only server, for example to one of the government servers mentioned above, they had to verify themselves to create their account on those servers
Each Mastodon account can create verified links to their official website
To verify yourself as the owner of a link in your profile metadata, the linked website must contain a link back to your Mastodon profile. The link back must have a rel="me" attribute. The text content of the link does not matter.
As anyone can set up fake websites and then successfully create a verified connection between such a fake site and their Mastodon profile, it is not 100 percent reliable.
It is helpful to check for the following: If you click the Mastodon verified link, does its URL in your browser exactly match the URLs that you may find through their officially verified accounts on a different platform? Do other links from other reliable sources like news media match exactly? Or in cases where real life products featured their URL, does it match exactly with their Mastodon link?