This probably sounds like a strange question, but I've sometimes heard it said that a book or movie "explores" the themes of this or that thing, and I wonder: What the hell does that mean? I'm not big on literary interpretation, so things like that kind of go over my head.
Usually when people use that expression it means the medium takes a deeper look into the theme. When you "explore a theme" you generally have to know a lot about it (whether or not you have to research beforehand or just know) and then you try to flip everything on its side and take a different approach. An example of this is I explored the theme of Schizophrenia and other mental illnesses in Shakespeare's work in a college paper. I took everything I knew about his work and looked deeply into it through the lends/theme of the characters having mental illnesses.
It basically just means that a work is about the theme. I think of my uf WIP as 'exploring' themes of found and legal family because it deals with the MC and other characters coming to terms with abusive / neglectful / deceased legal families and finding a surrogate family of close friends. You could say ATLA explores the concept of family in a similar way, given how all the members of the gaang are distanced from their families in one way or another but obviously regard each other as family. 'Explore' just sounds cooler
Another example of exploration of a theme is Ghost in the Shell. The Major's body is all machine apart from a portion of her brain (and not a big one if I recall), so the franchise deals a lot with where humanity lies and the notion of having a soul. Stories focus on a central conflict, a theme could be the root of this conflict or something characters go through as a result.
It's like how you make commentary about a theme or issue by portraying it in your story. For example, the Faith Militant group in Game of Thrones explores the theme of what can happen when fundamentalist ideologies take over a society. The way Sam's father reacts toward Gilly being a wildling explores the theme of discrimination. The way the Dursleys are portrayed in Harry Potter explores the themes of child abuse, favoritism, and conformist/sheeple living.
Basically: showing people something that they didn't know about a concept. One scene from Season 2 of Daredevil explored the theme of PTSD. Frank Castle had just been arrested for his rampage as "The Punisher," Nelson & Murdoch have taken him on as a client, and Karen Paige is with him discussing defense strategies. She brings up PTSD as the basis for a potential insanity plea, Frank shuts her down, and the implication (going by the most popular narratives of PTSD in our culture) is that he's one of those insecure alpha-macho types who thinks it's shameful to suggest weakness. What really happens next is that Frank says he's seen PTSD as a soldier, he's seen what it's done to the men and women he's served with, and he's not going to insult them for what they're going through by reducing it to a legal brownie point when he knows for a fact that saying he has the same problem would be a lie. That's not a perspective on PTSD that most people are shown by fiction or by most of the people in their real lives, and that makes it something that more people need to be shown. I'm hoping to do something similar in my own work, but from the opposite direction: Spoiler One of my villain protagonists was raped at 15, ran away from home and lived on the street for a few years, then over the course of her early 20s made a name for herself as the Deadliest Female Serial Killer in American History. She would be the first to admit that group sessions and anti-anxiety meds did more to bring her out of PTSD than committing her own violence ever did (contrary to the popular narrative that if you're ever subject to horrifying violence, then all you need to do is go on a roaring rampage of revenge and then everything will be OK), and she would bash your head against the wall if you ever told her that being raped and developing PTSD turned her into a serial killer (contrary to the popular narrative that "s/he was raped" can be thrown casually into a villain's origin story just for shock value).
Okay, I get it now. Thanks. I was wondering a bit because my story deals with racism, to some degree - it's not a central theme, but it does impact some of the characters and helps define how they develop throughout the story. I don't think I'm "exploring" it, though, just using it as a meaningful plot device - it's not gratuitous, and it does serve a purpose.
In my view, it's a thorough testing of an idea. And I mean thorough. It's something you equally THINK about and ACT within while your (characters') thoughts and actions at all times - if perhaps inconspicuously - serve a larger idea than themselves. It also influences you. If your theme is to embrace the dark side of you, you'll end up creating darker characters. But that's the lower dimension. If you wish to EXPLORE that theme, you'll create a main character who IS dark and struggles with it. And you'll focus on creating characters who not only mirror that darkness, but you'll also make THOSE characters complex. Maybe their darkness affects them. Maybe their darkness has a light at the end of the tunnel. Maybe darkness is temporary. Maybe darkness is our friend at times. Notice each of those sentences has the word "darkness" in it? That's theme.
Crime and Punishment explores the theme of guilt and doing what is right, about how we justify our actions, and equality. It is not simply about a murder and robbery.