You see the approval status if you go to the My Time screen in the Time Review tab,

The Salesforce Administrator at your org can write triggers to send an automated email to the users and inform them of status changes.

We will be implementing a feature in the PK4 TimeTracker application, where an automated email is sent to the user on the Status change, so the user will know if the time details are Approved, Rejected or Awaiting correction status. And it will be implemented in the future release of the PK4 TimeTracker app.