What should I enter as server URL? I have a Drupal site on Amazon server. On the amazon server, I have created an Elasticsearch server. I want to connect my Drupal instance with that server so I can use the search server for performing the search operation on the site.

I added and configured the Elasticsearch connector module which, in order to connect to the search server, needs I create a cluster which would help in connecting both the instances.

While adding a cluster to the Drupal instance, it asks me about the server URL. I am not sure on what I should write as server URL. What should I add in that form field?
Just enter the Endpoint of your AWS Elastic-search Cluster.

Use port : "80".

the Complete url will be something like: 

XXX-XXX-XXX-XXXXXX.ap-southeast-1.es.amazonaws.com:80

First check are you able to access the Elastic-search , Try to telnet on the server:

telnet XXX-XXX-XXX-XXXXXX.ap-southeast-1.es.amazonaws.com 80

If it's not accessible make it available for your IP by changing the access policy .