In philosophical terms, "agency" is the capacity for a person to make decisions and act according to those decisions. The ability to decide one's own actions entails a substantial degree of self-expression and so is quite a significant power to hold, both pragmatically and existentially.
In videogames, however, agency becomes a tricky thing. Virtual actions are the products of the agencies of multiple participants: the player who acts, the developer who enables actions, and in cases of story-based narrative, the player-character whose actions drive forward the plot. For instance, players often distinguish between things they did and things their character did. When these agencies line up in agreement, a game is poetry in motion.
Not so much when they collide, as occurs in the puzzle platformer Ico, a game haunted by the agency quandary. The illusion of choice granted the player only survives so long as the player wishes to act according to the developer's guidance, and when the player's desire on how to act strays from this guidance, the illusion shatters beneath an unveiled deterministic game design. With the player's actions largely being governed by the whims of the developer, player agency becomes something of a problem.