This may sound like a complex question, so let me explain what I mean. I'm inspired by Harry Potter, Avatar The Last Airbender, Homestuck (it exists), and all of those things have different houses / nations / classes / etc that have their own philosophy, ideology, and symbolism to them.
For example: Ravenclaw (my house) has the ideology of thinking outside the box, it has the symbol of a raven which shows intelligence, it's colors are bronze and blue which shows 3rd place and "once in a blue moon", etc.
I'm using this kind of storytelling to have readers project themselves onto the world, I.E. Through fanfiction (don't laugh) and personality quizzes. I'm using it to give an amount of depth to the world. They would also (as you guessed) have some symbolism and motifs to them.
How can I incorporate these things into my story?