A month ago, Google announced it is slowly getting into the domain name registration business through Google Domains and offered a form to sign up to be invited.
Well, some have been invited over time but now those who have had access are now being given the ability to invite friends and colleagues. I believe this is flowing mostly out of Googlers who have accounts with Google Domains.
For example, John Mueller is asking if certain folks want invites to Google Domains on his Google+ account. I know other Googlers have offered invites to others as well.
It seems like this Google Domains rollout is working a lot like the Gmail invite system.
Kim Clinkunbroomer posted on Google+ a screen shot of the interface for Google Domains:
I also believe GDG Kansas City is sending out invites tomorrow, learn more about that on Google+.
Forum discussion at Google+.