Google recently launched Custom URLs on their Google+ platform. They were available with a limited number of partners at that time.
The rollout is now broad with thousands of more users included this time around. If you are a verified user on Google+, you are more than likely to see an option to pick a custom URL for your profile/page.
Google developer Saurabh Sharma said:
We’re making these changes over the next few days, and we’ll be offering custom URLs to many more profiles and pages in the future. We appreciate your patience in the interim, and we look forward to hearing your feedback!