Between January, 2011 and November, 2015, the Drupal community built Drupal 8, an upgrade to the Drupal Content Management System. The system was redone from the ground up, replacing some core functionality with the Symfony PHP framework, moving configuration out of the database and into the file system, replacing PHPtemplate with twig, and much much more. So much so, that it is nearly unrecognizable as Drupal.
Jen Lampton and Nate Haug decided that there was a need for a CMS that more closely resembled Drupal 7 and decided to do something about it. They chose a key point in the Drupal 8 development, created a fork of Drupal, dubbed it Backdrop, and started to work towards a 1.0.0 release of their own. (You can read the whys and wherefores in her own words here.)
I agree with them. Drupal 8, while a powerful and impressive CMS, was too much too fast. Drupal 8 is what I would expect Drupal 10 or Drupal 12 to be. More than just say, "I agree with them," I also support the project with code, both in Backdrop core and porting contributed modules that I maintained or co-maintained for Drupal 7.
If you were to ask me which is better for a new project, Backdrop or Drupal 8, I'd say neither. As of this writing (May 30th, 2016), both suffer the same problem -- a small pool of contributed modules compared to what is avaiable for Drupal 7. Drupal 7 has had over five years for the community to create a rich collection of modules that extend the capabilities of the core Drupal 7 code, over five years for developers and site builders to use and write blogs about them, over five years for poeple to find all the quirks and issues. For projects that want to maximize available features and minimize development risk, Drupal 7 is clearly best.
Backdrop, however, includes a Drupal 7 compatibility layer that makes porting modules from Drupal 7 to Backdrop much easier, often times trivial. For example, I was able to port Date/Time Help, albeit a very simple module, with two lines. The compatibility layer bridged the gap between Drupal 7 and Backdrop so well there was essentially nothing to do. Thanks to the compatibilty layer, I can give Backdrop second place because it has easy access to the pool of Drupal 7 modules.
Over time, both Drupal 8 and Backdrop will catch up to Drupal 7 and the question will come down to the needs of the client. Popular opinion is Backdrop offers a simpler and lighterweight system ideal for small to medium businesses, non-profits, clubs and social groups, while Drupal 8 will provide stronger internationalization and enterprise-level scalability.
Sentai Digital is proud to support Backdrop CMS.