The Stage field is one of the most important fields from the Seller Leads app. It's used for categorizing the Seller in different stages from the New Property. 

Each lead that will be created inside your system, will be marked with Stage = New Property. That way you will know which lead is a new one and which lead already exists in your system.

The Stage = Appointment Booked is used when you have an appointment scheduled with your Seller Lead (check the Appointment section of your Seller Leads app). As soon as you schedule the appointment the Stage will change to Appointment Booked.

The Stage is marked as Contract Signed  when a new Closing item will be created form the related Appointment (in the Appointments app, if Status = Completed - Converted). Manually setting the Stage to Contract Signed will also generate a new Closing item and attach it to the Seller Lead.

The Stage is marked as Follow-up when you have a Seller Lead that you need to follow up with. The Stage of a lead is automatically changed to Follow-up if on the related Appointment item the Status is changed to Completed - Not Converted or Canceled.

The Stage is marked Closed automatically when in the related Closings item the Purchase Status is changed to Closed.

The Stage is marked Dead when a lead wants to be taken off your list or you want to mark it for deletion. The Stage automatically changes to Dead when in the related Closings item the Purchase Status is set to Canceled.

As you can see, you don't have to manually change the Stage field because it will be automatically changed along the way :)