Final answer:
The passage explains the origin and characteristics of the waltz dance, which identifies the author's purpose as explaining something.
Step-by-step explanation:
The author's purpose in the passage given is to explain something. The passage provides the etymology of the word waltzen, details what specifically makes a dance a waltz, and describes the basic foot pattern. This explanation helps the reader understand the historical and cultural context of the dance, making option D the correct answer.