What does first edition first state mean for Wizard of Oz books?

Simplified, first edition means all copies of a book (any book, not just Oz) printed any time from one type setting without any changes.

A state is a variation in a book, but still within the same printing. When books were manually printed, minor changes may have been made in the middle of a print run. For example, if after a number of copies are printed, the printer sees that a Word had been misspelled. The type for that Word alone would be changed. A new printing would not be necessary for something this minor. Copies before the correction would be considered the first state. Copies after the correction would be considered the second state.

If a book doesn't change it is still the same edition. So, if an author changes the text, or if the pages need to be re-done for a paperback's smaller size, then substantial changes have been made and it's a new edition.

When the publisher runs out of copies and prints new ones without making changes, then the edition is NOT changed, but now it is a new printing.