Contact Stage is a contact (client) property that indicates where a contact (client) is in your marketing/sales funnel.
There are 2 ways in which you can change the Stage of a contact.
Option 1: To change the contact stage from the contact list page.
Select a bunch of contacts whose Stage you want to change and click on the "Update Field" button
Select the "Stage" option from the drop-down
Choose an appropriate Sales Stage from the list and don't forget to hit "Submit"
Option 2: From within the contact
Click on the Contact name
Click on the drop-down that is towards right of the contact name.
Here's a short video on how to do it!
This will help you monitor your sales pipeline.