CANZUK stands for Canada, Australia, New Zealand, and the United Kingdom. Specifically, it is about a proposal for closer political ties—including free movement—between these countries.
I don't normally sign or share petitions, but there is one for the CANZUK concept (HERE) that is gathering momentum. I think it's a great idea worth promoting. Such a policy would provide many opportunities for citizens of these countries; and our similar cultures and levels of economic development should minimize the challenges and tensions that sometimes accompany human migration.
If you're interested in learning more about the concept, a book (more of an extended pamphlet, really) that I read last year fleshes it out.