The "Enrollment ends on" section in the Program Editor does just what it says: It ends enrollment and hides the Program from the Enroll Form starting at 12:00:01 AM (your company's time zone) on the date you enter into the box.
People typically use this field when a Program runs for a specific amount of time and they want to close enrollment on a particular date in the future.
For example, Summer Camp runs from June 1-July 30. You want to open enrollment from April 1st - May 27th. In this case, you would add May 28th (meaning the Enroll Form will allow enrollments until midnight on the 27th and then close on the 28th) in the Schedule section under the field labeled "Enrollment ends on" (see below).