I am on a shared hosting on HostGator and now I want to take one other shared hosting on some server and want to put only the images used on my site to it. So that those http requests of images could go to another server, is that possible? and how? thanks.
What you are looking for is called "CDN" or "Content Delivery Network".
Here is a WIKI! definition if you are not familiar.
There are plenty of good tutorials out there that will show you how to carry this out using Wordpress.
Here is one you can have a look at.