The inbox is a feature that came for free with the Reddit codebase but it was "lost" when the site was restyled. You will notice that the formatting of inbox page is totally messed up, this is also because it wasn't included in redesign. Notification of replies is on the list of things to implement but there's some higher priority work going on at the moment. Since it is a small change and many people seem to be requesting it I hope that we will get to it soon.