Something that isn't recorded officially is unregistered. If your car is unregistered, you can't legally drive it.
When you put something on an official list or enter it into a directory, you register it. Leaving it off such a list makes it unregistered. In some cases, this isn't a big deal — your puppy, being a lovable mixed-breed rather than a fancy purebred dog with the official paperwork to prove it, is unregistered. But when it comes to things you're required to register, like cars and guns for example, being unregistered is a real problem.