What might be the problem with the authorization of my laptop while syncing the iPhone? I tried to sync music onto my iPhone using iTunes. 

The process was halted by a dialog box that said my computer wasn't authorized to sync the iPhone, so I have to authorize it. I did that and again tried to sync the iPhone, but the dialog box appears every time and the syncing process gets stopped.

Is there something up with iTunes or is the problem with the iPhone? I'm running iOS 7.1.1.
I suspect that you have multiple purchased items from multiple Apple IDs which would explain the multiple messages. Did you authorize your PC for only a single Apple ID? Try to authorize it with a different Apple ID each time you are returned the dialog box.

Of course this implies you indeed have multiple Apple accounts and know the user name and password for each one of them.