Call it what you want. Subtext. Exposition. Deep meaning.
My screenwriting professor, like so many other before him, insisted that you "Show, don't tell." And he was right. The things you don't write tell the story more than the things you do. No story worth reading or watching pontificates the narrative to you. Every decent story layers action and dialogue in such a way that you piece together important pieces rather than being spoon-fed what's going on.
It's really a matter of not underestimating the intelligence of your audience. Talk to people like they are simpletons even if your demographic are young children, and they'll reject your story as idiotic...which it is. Respect them and let them read between the lines...and even the ones who don't understand everything going on will enjoy what they do understand.