YAD7 is a community-sponsored answer to The Drupal Organization's announcement of End-of-Life for Drupal 7. Because Drupal is open-source, the community has the opportunity to decide whether to go along with the main-line branch (currently in version 8 and moving towards version 9), or whether to pursue a different course. Given that there are about a million Drupal 7 sites, and that the migration path to Drupal 8 involves a profound redesign of existing sites, the Drupal community needs a more compatible migration path forward.
The YAD7 fork of Drupal 7 provides this. Initially, YAD7 is nothing more than a simple fork of Drupal 7 and all Drupal 7 sites should be exactly compatible in all ways with YAD7. Furthermore, YAD7 will remain a simple downstream fork of Drupal 7 until the moment that Drupal 7 reaches the end of its life as defined by the Drupal Organization.
At the moment that Drupal 7 becomes unsupported, YAD7 will assume the mantle of providing security releases and a migration path forward, without abandoning all of the many Drupal 7 sites that would otherwise require a resource-intensive redesign.
There are many ways to install Drupal 7 and YAD7. The main distribution point is the Github source for YAD7 Drupal 7.