This is the name of the client that will appear on the invoice.
As you begin to type the name, previously used names appear as options. If the session is with someone you have previously had a session with, then you can just choose that name from the drop-down menu. If it is a new person, the menu will offer the option to add them as a new client and will open up new fields to fill in so that you can register their details.
If the selected client has had a previous session, then the same session details will be filled out for you. You can modify these as needed.
Alternatively, you can register the person first in the Clients section and then book them in to a session afterwards. This will allow you to include additional details that are not included on the Sessions booking page.