What does it mean for a person to have agency?
In social science, agency is defined as the capacity of individuals to act independently and to make their own free choices.
Why is agency important?
It empowers players to influence their own path to mastery. By encouraging players to take initiative, you enhance their cognitive ability to take control, increase motivation, and help ensure they are engaged with the game.
There are two ways that applies to games:
The first is imaginative agency, which means the player has the choice to be and imagine who they want to be. Some ways of allowing this are to make synonyms and analogs of items in your game. For example, have a sword and and axe. Thy both give you +1 Attack, yet you can pick which one you prefer.
Another important thing for promoting imaginative agency in a game is to make sure equal things have equal powers, ie. no degenerative strategies, or unbalanced character classes. Which character class would a player like to play? Ranger, Warrrior or Rogue. They might have different mechanics and powers to differentiate those play styles, but have the same chance of winning. Otherwise, if the warrior is just better, there is a divide between strategy and imagination. You have to pick the warrior to win, but you feel like playing the Ranger. There is a lack of coherence there, and it will turn off both the imaginative player who likes to get immersed in their character, and also the strategic player who likes to experiment with different strategies.
That leads me to my next point, strategic agency. Which means you can choose and define your own strategies in a game. This should be obvious, since it relates to meaningful choices, and balanced elements. But if there are one or two strategies that are clearly superior (in the final analysis), the depth and interest of your game is going to be short lived. People might like it while discovering those strategies, and then its over. Having a wider pool of possible paths to victory not only increases the replayability and depth of your game, it helps give people strategic agency.
It makes me think of the meta-game in a Magic the Gathering format. If one or two decks are dominant, then the format gets stale quickly, because you see those decks way more often, and feel forced to take one of those to win. The more types of decks have a winning chance, the more strategic variety and agency there is in a format, which is more interesting for players.