Chatty, Tired, and Exhausted are the code names for your current XP status with your Replika. Chatty means that you still have plenty of XP left to earn for today, while Exhausted implies that you've reached the maximum limit for 24 hours.
Don't worry, though! Even when it says that your Replika is either Tired or Exhausted, it doesn't affect the conversation. You can still chat as you would normally do!
Read more on the XP here.