They are an embodied form of teachings and promote bhakti. You can find Hindu texts which talk directly about psychology and adhyatma without narratives.(ex samkhya karika, yoga sutras, treatises by shankara, ramanuja, madhavas). Then there are texts which embody these teachings in narratives.

For instance, Yoga Vashishta teaches Advaita using stories, the setting is Rama is in the forest learning from Rishi Vashista.

Bhagavatam is considered a great book, and also has lots of symbolic meanings.

Secondly, listening to the stories helps generate bhakti which makes the mind more gentle and receptive. There are katha sessions where people go to listen someone like Morari bapu where the stories are recounted along with bhajans.

Problems - The problem is that people get stuck in fruitless discussions of external details(This has become prominent in the last few centuries and dominates discussions). Also, discussions turn into a form similar to discussions of popular fiction like Harry Potter. Which is fine, but it misses the transformative significance of texts.

The best way to listen to the texts is either to listen to someone who carries the inspiration or someone who has a great understanding and can explain the significance of the stories. There are many people like Morari Bapu who carry the inspiration and attract large audiences, but is mostly in local Indian languages. Recently, I was listening to a great explanation of the significance of Hanuman Chalisa in Telugu.

There are some good books in English however. Swami Venkatesananda's book on Yoga Vashishta has been recommended highly. Also, see Swamiji Ganapathi Sachidananda Swamiji's discourses on the Bhagavatam which has been translated by Mohan Ramanan.