In an active/passive configuration, systems are set up to bring additional resources online to replace those that have failed. For example, OpenStack would write to the main database while maintaining a disaster recovery database that can be brought online in the event that the main database fails.
Typically, an active/passive installation for a stateless service would maintain a redundant instance that can be brought online when required. Requests are load balanced using a virtual IP address and a load balancer such as HAProxy.
A typical active/passive installation for a stateful service maintains a replacement resource that can be brought online when required. A separate application (such as Pacemaker or Corosync) monitors these services, bringing the backup online as necessary.