Docker_ElasticSearch_Kibana.txt

https://github.com/docker-library/kibana/issues/65

Correct, your host can access elasticsearch via localhost since you forwarded the ports with -p 9200:9200 -p 9300:9300, but kibana has its own network interface and localhost in the kibana container is just kibana, not your host.
You need to either give the ip of your elasticsearch container to kibana:

$ docker run -d -v "$PWD/esdata":/usr/share/elasticsearch/data -p 9200:9200 -p 9300:9300 --name elastic elasticsearch
$ ip="$(docker inspect --format '{{ .NetworkSettings.IPAddress }}' elastic)"
$ docker run -e ELASTICSEARCH_URL="http://$ip:9200" -p 5601:5601 -d --name kib kibana
or use linking dns so that kibana can resolve a name to elasticsearch:

$ docker run -d -v "$PWD/esdata":/usr/share/elasticsearch/data -p 9200:9200 -p 9300:9300 --name elastic elasticsearch
$ docker run --link elastic:elastic-url -e ELASTICSEARCH_URL="http://elastic-url:9200" -p 5601:5601 -d --name kib kibana
or docker dns on a network:

$ docker network create elk
$ docker run -d -v "$PWD/esdata":/usr/share/elasticsearch/data -p 9200:9200 -p 9300:9300 --name elastic --net elk elasticsearch
$ docker run -e ELASTICSEARCH_URL="http://elastic:9200" -p 5601:5601 -d --name kib --net elk kibana