As Kit Eaton reports"Vanity" URLs have been available to some high-ranking Google+ users for a while, but now Google is dramatically expanding the system. This means you will likely be able to customize your account page with a more memorable address. Instead of a bunch of meaningless numbers, users' URLs now look like:http://plus.google.com/+Username.
Google is rolling out the system to users right now. To get one, you must verify your Google account with a phone number, have had an account for at least a month, and have at least 10 followers.
I think this is a very big move for Google. The vanity URL makes it easier for potential followers to find you on Google+. More significantly, it makes the Google+ network a more human place. Owning your Plus homepage is now a more touchy-feely experience because, for example, to share your account details you don't have to email someone a stupid machine-like string of numbers to tell them the address of your Plus profile. It's also the sort of label that can go on a business card or in an email footer.