I was wondering is there way i could start my application (that stays in background).Dial some number from dialer and the application could know what is being dialed.
No, you can't do that, not in the Apple way. And also anyone should not be able to do this, as this will be a major security / privacy threat. If this was able then it would be easy to collect all the numbers the person dialed and then send them to my own server.