This feature was introduced in CRM 2013 SP 1.
Routing rule can be used to route a case to user/team/queue when it meets a pre-configured criteria. This functionality is really nice for automatically assign cases to different queues, however, the automatic routing rule execution is not quite straightforward.
Normally to invoke this functionality, users have to select the case(s) and click Apply Routing Rules button.
For the routing rules to be invoked automatically, the cases must be automatically created via Automatic Record Creation Rules. Plugin or Workflow created cases are not considered automatic!