"Rosebud!" The famous, first murmured word from Orson Welles' 1941 cinematic masterpiece Citizen Kane, is a plant, only to be paid off at the end of the film when it's revealed that the enigmatic "Rosebud" was Mr. Kane's childhood sled.
Planting and payoff is a device by which a motif, a line of dialogue, a gesture, behavioral mannerism, costume, prop or any combination of these is introduced into a story and then often repeated as the story progresses, until in the changed circumstances toward the resolution, the planted information assumes a new meaning and "pays off".
Incorporating planting and payoff is a key ingredient to a good script: future & advertising, mystery & suspense, delay & revelation, and preparation & aftermath are all tricks of the trade that use planting and payoff to help create a strong audience connection. And the audience is everything. It's why you write the script in the first place, and as the screenwriter, it's your job to make sure you do everything possible to help the audience become invested in the story by making them feel smart, anticipating, reaching conclusions, and adding it up.
When planting and payoff is used correctly, the audience doesn't realize they are working it out, but they are. No longer are they passive passengers. When you allow your audience to add up two plus two, they will love you for it - because you created an opportunity for them to become connected and intimately involved in the story.