How can literature help us reach a deeper understanding of ourselves and our growth as moral and ethical people?

It helps you see the world from multiple people's viewpoints. You get to experience their backgrounds, their pain, their joy, and what makes them tick.

As you read how characters interact with one another, and how they create and resolve conflicts, and how they overcome obstacles, you can examine your own reactions to a character's actions. Do you agree with what they did? Even if the situation is something you have no personal experience with, imagine what you might do. Put yourself in the place of the various characters.
And if you have had a similar experience, honestly consider your actions. Could they have been different? How might the outcome have changed?
Literature helps us explore human nature-- triumphs, shortcomings, and failures. We can uncover the thematic message the author communicates to the reader, gain new perspectives, and learn from the experiences of others-- even if they are fictional.