Further Explanation
about the title: Morphology of the Folktale
Morphology: the study of the form, shape and structure of something.
The Folktale is somewhat misleading as it covers a much broader range of material than Propp is classifying. This is an error of the translators as Propp clearly defines the set of tales he's working with at the beginning of chapter 2.
Propp also dislikes the term "fairy tale" as it only applies to a subset of tales he examined, but he uses it for lack of a better convient term.
Propp's theses
Function: An action of a character, defined from the point of view of its significance for the plot.
about the "fairy" tale
The identifying features of the "fairy" tale are it's:
Based on: "Morphology of the Folktale by Vladimir Propp" (University of Texas Press, Austin, Texas, 1968)