What do the schedule numbers on each record represent on the 1939 Register?
The 1939 Register, much like the decennial censuses before it, was actually compiled from household schedules. The enumerator dropped off the schedule to each house a few days before National Registration Day (29 Sep 1939). The format of the schedule looked like this:
Each schedule in each enumeration district was assigned a unique number, typically in the order the schedules were given out. This is the schedule number.
The schedule sub-number shown on the Register is simply the order that the names were entered onto the household schedule. That is, the third person on the schedule would be sub-number 3.
All members of the same household have the same schedule number because they were all entered on the same schedule.
The householder filled in the schedule, and the enumerator came to pick it up after National Registration Day, correcting any details as needed. The enumerator then compiled the schedules into the 1939 Register that we can access today.
The original schedules were apparently destroyed; see What happened to the original household schedules used to produce the 1939 Register?
It's simply a way of distinguising households/institutions.
According to the National Archives
Information is arranged by:
enumeration district – each enumeration district has a unique four- or five-letter code, and large enumeration districts may comprise more than one book
household or institution – each household or institution is represented by a schedule number. A large institution such as a hospital may be an enumeration district in its own right national
registration number – each person is represented by a sub-number within the household or institution