There’s no part of a story more exciting than the Rising Action into the Climax, so writers tend to put all their effort into that lead up… which sometimes means that the "Falling Action" doesn’t get nearly as much attention. The exciting part may already be over, but the Falling Action is just as important, so you need to know what it is and why it shouldn’t be overlooked.
"Falling Action" is what happens in a story directly following the Climax as all that tension you built winds down. In the structure of Freytag’s Pyramid there is a distinct difference between Falling Action and the "Resolution," where the story actually concludes.
The Falling Action and the Resolution exist in most all structure outlines in different forms, and what defines the Falling Action is that it is not "the end" but a deescalation of the main conflicts and the tying up of any loose ends. If anything that was built up in the Rising Action is not used in the Climax, it should be addressed in the Falling Action. Even if that is simply passing a topic on to the next book in the series, the Falling Action would be where you make readers that promise, or dissolve its necessity.
Even if readers have a blast going on the literary adventure, how your story ends is the last thing they experience, so they will notice if the final parts are slapped together as an afterthought, sullying their lasting impression.
Falling Action is the buffer to smooth out any potentially harmful hindsights readers would have upon completing the story.
For example, if you spend an extensive amount of time on a certain setup that doesn’t come to fruition, you could address that in the Falling Action so readers don’t feel like the misdirect was a waste of their time. The Falling Action can answer any outstanding questions, or assure that certain plot points will be relevant later.
Regardless, spending a lot of time developing into the Climax only to have the aftermath quickly brushed under the table is not very satisfying. "And then they lived happily ever after" as soon as the villain is defeated is too abrupt. The Falling Action exists to lead into the final Resolution for a reason: pacing and reader fulfillment.
If the Resolution is the bow on top of a gift (your story) then the Falling Action is how well you tie it—and presentation matters.
If you want to write Falling Action well and leave readers satisfied with the eventual Resolution, keep the saying in mind that "every action should have a reaction." Alternatively this could come in the form of consequences for character’s earlier decisions, long-standing reveals (that weren’t in the Climax), and any unresolved elements.
Keep track of everything that is introduced and happens in the Rising Action, and acknowledge it in the Falling Action. This does not need to be an outright mirror or counterpoint of what came before—essentially, just don’t leave any glaring questions unanswered or promises unfulfilled.
Although all stories can be boiled down to such a simple structure, thinking about your story in terms of Freytag’s Rising Action and Falling Action may not be your preferred method of planning. Keep a satisfying Falling Action in mind, but plan however suits you best—here’s a list that summarizes various other $ outlining techniques$ to get started and see you through to the end!