Mastodon allows me to verify that a link belongs
to me by adding a simple rel="me" attribute to the HTML
code. Since this page is hosted on a domain name I’ve and controlled
since 2010, the presence of this link on my Mastodon profile helps to
verify my identity within the fediverse.
Put simply, this page claims that I am the owner of specific Mastodon accounts. Those Mastodon accounts have profiles which link back to this page. Since I have final authority over this domain name, you can be reasonably certain that the domain and the accounts all belong to the same person (me). If you have been following me or otherwise connected with me enough to recognize the domain name simonj.me, you now know that I also control the Mastodon account in question.
On each of these profiles, you should see a link to this page along with a verification that this link belongs to me.