The play of a RPG is all about the establishment, and ongoing generation of, a fiction. shared among the participants. It's this fact of fiction that is one of the things that distinguishes RPGing from boardgaming, or purely mechanical wargaming.
The ongoing generation requires the fiction to be created. This is what RPG procedures do - and as I posted, in a pretty conventional/mainstream RPG, the two main modes of creation are (i) the GM narrating a new scene/situation/encounter, and (ii) the actions that the players declare for their PCs generate consequences.
How are these things done? Who establishes what the elements will be, what the themes will be, how they are related, what possibilities they open up or foreclose? These are some of the elements of control.
If all the players influence is what their PCs try to do, then as I said they have the bare minimum control that is consistent with the game being a typical RPG at all. But that doesn't have to be all. It's not all the players can do in Gygaxian dungeon crawling, for instance: when the players are in the process of obtaining information, it is the GM who is controlling the information; but when the players exploit that information to achieve their PC goals (in virtue of their knowledge of how their declared actions will resolve) they are able to exercise control. In effect, they are able to oblige the GM to narrate the things that they want to be part of the fiction (to give a very simple example: by saying "I lay a plank over the pit", and then "I walk over the plank", the player obliges the GM to narrate "You get to the other side" rather than "You fall down the pit").
The idea of making a move that obliges someone else to make a particular move or at least constrains their move space is a fairly standard part of game play. In chess, by checking the opponent's king, I constrict their move options. In bridge and similar games, by choosing what to lead I control the play of the cards, exploit my length in a suit, run those who are short-suited, etc.
In Gygaxian play, the players aspire to get to a level of knowledge of, and position in relation to, the fiction that they can similarly control it. (Which, in this context, isn't the same as narrating it. Just as I can control your play in bridge, without being the one who plays your cards.)
Burning Wheel uses a completely different set of techniques to also allow players to exercise control over the shared fiction.