Agency
Also said as Player agency, Meaningful choice
The player's power to change what happens in a way that matters to them. It is measured by what is different afterwards, not by how many buttons were offered.
Agency is the one thing a game has that a film does not. Take it away at the moment the player cares most and they stop feeling like the cause of anything.
Say it
“Give the player real agency over the fire: which houses burn depends on where they send the water, and the closing scene names each house they saved.”
Where you’ve seen it
Undertale lets you spare every monster you meet. The ending, the way characters treat you and even the shape of some boss fights follow from what you did.
Not to be confused with freedom
Freedom is how much you can do. Agency is how much of it changes anything. A huge open world where nothing reacts has plenty of the first and little of the second.