It's technically the domain for Anguilla, a literal British colony in the Caribbean.
It appears to be managed by some random guy- check out the .ai registration FAQ: http://whois.ai/faq.html
If you are going to use .ai, just be aware the top level of the domain appears to be managed by some dude with a gmail account. Its not necessarily bad, but something to consider if you're planning to host your billion dollar AI startup on it.