Question

How does dividing the article into sections help the author develop the article's ideas?

Answer 1

Dividing the article into sections help the author develop the article idea BY UNIFYING EACH PART AND FOCUSING ATTENTION ON ONE TOPIC AT A TIME. 
Dividing the article into sections will help the author to treat one topic at a time and to concentrate fully on that topic. Smooth transition from one topic to another throughout the book will gives the book a unifying touch.

Answer 2

The answer to your question, How does dividing the article into sections help the author develop the article's ideas?, would be It unifies each part and focuses attention on one topic at a time. This will help the author organize his or her ideas and the readers to understand the article.