Review process for comments on an article
The procedure is quite common, and frequently comments and response to comments, if significant, are then published together. 


  Now my query is, why and for what purpose they are seeking response from author of paper ? 


Why shouldn't they? You are actually criticizing their work, highlighting some flaws. You might be right, you might have misinterpreted their paper, or you might be plainly wrong: whatever the case, it's fair to allow the authors to reply to your criticisms and explain their point of view, if different.


  Although I have no problem with that but I am curious to know, how that author would responds to my comments on his/her paper ?


Well, there's no general answer for this: it depends on the kind of comments. Sometimes they might simply acknowledge the issues, whereas sometimes the authors write another commentary explaining why they think the comments are wrong. And sometimes the two parties reach a common point of view.