.library
-> This something like you would like to load your extra js on the site
e.g. when i call this

.library("markitup")

, it will call load this js lib file.
../media/com_easysocial/scripts/vendors/markitup.js

.module
-> It like a declare the script namespace (this can be any name) so that you can call this name in any Easysocial page.
e,g.

EasySocial.module("story/blog", function($){

  xxx

}

.script
So other page you can use this namespace to call, it like a call the module that was declared above

EasySocial.require()

.script("story/blog")

.done(function($) {

xxx

});