Depending upon what classic period is being referred to, the insistence on emotional experience is of the utmost importance. When looking at the literary movements of Romanticism, Renaissance, Naturalism, and Realism (given they have happened in the past-making them classic), authors and artists alike desired that their viewers and readers felt something very specific. For example, Romantics and Naturalists illuminated the power of nature within their texts (be it literary or artistic). These artists and authors needed a connection between their text and their reader/viewer. They depended upon their reader/viewer's emotions in order to insure engagement with the piece or text.
As for the Classical Period (which included the periods of Homer, Classical Roman and Greek, and the Patristic Period), poets and writers of this period also wished their readers to see both the physical beauty of their texts (with the use of the Heroic couplet) and the message of their texts.
Regardless of what one defines as classic, the aspects of classic aesthetic simply refers to the guidelines the period placed upon what should be included within a text in order for it to adhere to the categorization of other texts of the period or movement. All authors tend to look for some type of emotional experience within their readers. If they fail to achieve engagement of their reader, the authors work will never be able to spread its message.