You don’t want to explain to the audience, because that makes them observers. You want to reveal to them little by little and that makes them participants because then they experience the story in the same way the characters experience it. – Bill Wittliff
The theatre, for the most part, is verbal storytelling; therefore, it’s not uncommon for the playwright to tell the story through talking heads. But film is a visual medium, and the screenwriter must think cinematically. He can't write a bunch of description paragraphs on what a character is thinking. He can only write what we see, because in a movie, it’s usually not what a character says that is the most telling. It’s what the character does that really shows the story.
The old cliché is truth: action does speak louder than words. And it’s your job to describe the action cinematically. This doesn’t mean you should write in exotic locations, high-speed car chases, and a plethora of explosions – unless of course it’s a summer popcorn action film – but you still need to be visual, regardless of genre.
Say you’re writing a character-driven indie drama. Exposition may come out through a conversation, but you must avoid having two characters explain things while sitting in a booth at a diner, while laying in bed and talking from their separate home phones, or while sitting alone in the office break room at work. All those scenes are static. Have the same conversations, but turn them into arguments – a great way to get the past out is through conflict – and have this verbal smack down occur as your characters jog through Central Park, while on their cell phones running late for work and stuck in gridlock traffic, or navigating through office cubicles with everyone watching the fight.
Remember, film is a visual. At every opportunity, you must show, never tell!