I know for a fact that saved Kibana dashboards (ie, the JSON file of the dashboard) are saved in OR associated to a particular ElasticSearch
As others have said, you can find all of the objects that Kibana saves in the .kibana index within elasticsearch.
The most recent versions of Kibana 4 include an export and import feature that makes moving objects from one installation to another very easy. You can find this functionality by clicking the "settings" and then "objects" tabs.