I understand the use of article, section and aside tags on HTML5. In many ways, these tags seem to replace div tag we use on HTML/XHTML. Well, div tag is continued on HTML5 too. Where and when can I use div tag for more semantic markup?
The <div> element has no semantic meaning whatsoever. You can safely use <div> at any point where none of the semantically meaningful elements make sense.
A common example is a page layout wrapper <div id="wrapper">, whose sole purpose is to provide a visual wrapper for you to apply certain styles to.