Powerful Players, not Powerful Characters
Power in TTRPGs is hard to define. Under the ultimate authority of the GM, power can be granted and taken away in an instant. In rules-heavy games, many GMs are wary that their PC will become too powerful and disrupt the flow of the game. This is a valid concern, but it often leaves players who are just as powerless as their characters. This leaves the game dull, as having powerful players is what makes TTRPGs fun.
What makes a powerful player?
Powerful characters are those that are mechanically powerful. 27 AC and +12 to hit are both things that make characters powerful. However, they provide little for the player to engage with at the table. In addition, this power can easily be undone by the GM through adjusting target, enemy hit points, and the like.
Powerful players, by contrast, are those who are able to affect the game world. This "organic" power moves beyond character abilities and towards what an actual person would do in any given situation. Players have a great deal of inherent organic power, as they are playing humans (or vampires, androids, criminal bears, etc.) and are thus able to do anything a human can do. And when the game system lacks rules for certain actions, the GM creates rules for these actions. Anything a person can do, a character can attempt.
But organic power does not only come from human ability. It also comes from relationships, items, legends and rumors, and open-ended character abilities. Anything that players can use to affect the game world gives the player power.
Why Do We Want Powerful Players?
They're what set TTRPGs apart from other entertainment. The freedom to try things and strategize outside of strict mechanical considerations engages the player in ways that board/video games do not. The great strength of TTRPGs is the ability of the GM to make judgements based on actions outside of the mechanical framework of the game. This also makes the game less rigid and more true to life. In the real world, people take action, not activate abilities. When the game focuses on actions, the game world becomes less of a game world and more of "the world that the game is in". There's nothing better for verisimilitude than a game world that accepts every action and changes in accordance with them.
In addition to the fun and creative thinking gained by players, a game with powerful players is a game that is easier to run for the GM. When running for powerful players, game preparation focuses on creating open-ended scenarios rather than leading players to set outcomes. As the GM, it is also exciting to discover how the players interact with these scenes. With their power, players have near-infinite options to approach different challenges. Seeing the tools players use to solve these problems is what keeps me engaged as a GM.
How to Add More Player Power
The source of what makes players powerful is ingrained in the personality of the individual, and I do not condone brainwashing, mesmerism, hypnosis, or any other method to change the innate qualities of players. However, there are things we can do as GMs to encourage players to become more powerful parts of the game.
Give Narrative Control
The "I know a guy" rule. At any time, a player can declare that their character "knows a guy" who can help with the situation. The player has the freedom to create any detail about the character, but the GM holds veto power. This ability is often limited to 3/campaign, 1/city, or as a reward for good roleplaying. This can be expanded to "I know a place, legend, or item."
Prompt the players. "You enter the chamber of the grand priest and see him hunched over a desk. Vince, give me 3 adjectives to describe him". This works best when targeting a specific player; otherwise, each will be too polite to contribute lest they step on the toes of another player. In addition, when doing this, be mindful of which players you are putting on the spot; the pressure it creates is not always pleasant.
Provide Resources, Not Solutions
Resources are means of creating a solution, and the choices players make in crafting solutions are an exercise in their power. Resources is a general term that refers to actual items, but also relationships and allies, spells, and character abilities. Anything a player can use to change their character or the world is a resource. The more resources a player has at their disposal, the more powerful they are.
Give Alluring Descriptions To Items
Adding a few words to make items unique is an easy way to get players thinking about how they can use the items in clever ways. "The sword reflects light as sharp as a mirror" or"The vase looks regal, but is paper thin and fragile" provides enough detail to make the items seem useful without giving them an obvious purpose. Players must exert their power to use these items effectively.