Story Structure in TTRPGs

TL;DR, never call Act I an introduction. That's massively underexplaining what Act I is. Also, I worked out a really good reason not to play 5e D&D.

In story structure, Act I is the set up, Act II is the execution, and Act III is the resolution. 

In Act I, you set up the story. By the end of Act I, the themes, major characters, setting, conflict, stakes, and the goal should be established for the audience (or participants in TTRPGs). Act I ends when an event or action forces the hero (or by choice of the hero, but usually it's not their choice) to put their normal life on hold to engage with that conflict and pursue that goal. The number of choices available to the hero are greatest in Act I.

Act II is where you execute that story set up in Act I. If you set up a mystery, you execute the mystery, etc.  Act II is the longest act. Act II is about the hero engaging with escalating obstacles and risks in the setting as he pursues his goal. Obstacles (AKA trials) prepare the hero for their goal, first by testing the hero's skills and revealing his weaknesses or flaws, then by taking away his resources or nullifying his strengths, and by giving him lessons that make him stronger or wiser. Obstacles force heroes to confront failure; they force heroes to change or grow. Throughout Act II, minor characters and subplots may be expanded on or introduced, and are resolved before the end of Act II. During Act II, the hero's choices are narrowed down. By the end, the hero commits to one path. Act II ends when the tested and tried hero has overcome the obstacles and has learned from them, and is finally ready to confront the main antagonist.

Act III is where you resolve the story set up in Act I. It begins with a final confrontation with the primary antagonist that shows the hero's growth and how that growth made them worthy of their goal. Act III ends showing the audience the consequences of the hero's choices on the world; the world is not reset.

In good TTRPGs, Act I looks a bit like this: You ask the players what they want, give them some opportunities to get it, establish the obstacles that each choice will force on them, let them choose their preferred opportunity, then set them loose. I might even suggest working this into the ending of the previous adventure so that you start the next adventure with momentum. In D&D 5e, you pick one pre-written campaign book with a preset path and story.

In TTRPGS, Act II depends on the game you're playing. In 5e, you smash things, level up, gain powers, smash bigger things, level and gain more powers, and smash bigger things. Repeat until the second biggest thing is smashed and the players get some McGuffin. All while following a story that's already been written and is intended for general audiences.

In TTRPGs, 5e specifically, Act III is an obligatory fight with a damage sponge and a whole lot of cheap powers. Then you win the D&D. Seriously, why are you playing 5e? Stories are fundamentally about showing a character growing from a state of immaturity to maturity and imparting a lesson (a theme). Ever wonder why they call the moral of the story a theme? Stories are satisfying when a need for the growth is established in Act I, when the growth is earned through struggle in Act II, and when Act III reveals the results of that growth in a way that reinforces the lesson of the story. This character growth themes the story.