1a: the office or function of an agent; b: the relationship between a principal and that person's agent
2: a person or thing through which power is exerted or an end is achieved: instrumentality
3: an establishment engaged in doing business for another
4: an administrative division (as of a government)
Alternatively, and this is the more specifically "legal" definition, the word "agency" speaks of an arrangement by which one person (the agent) is officially commissioned by another, who is called the "principal," to act on behalf of the principal. There was a whole course on this kind of "agency" in my law school curriculum. Key questions included the responsibility of the principal for the acts of the agent, in various circumstances.
The Wikipedia definition captures this different usage in its listing titled, Agency (sociology):
In social science, agency is the capacity of individuals to act independently and to make their own free choices ... One's agency is one's independent capability or ability to act on one's will.
I haven't taken the time to research exactly how, when, or why this transition in word usage occurred, but I do find myself being surprised at what this expression has come to mean, as I hear students talking about their "agency," or some other person's "agency."
To my ear, "agency" in this more current usage sounds something like "personal freedom," or "my ability to take action."
Whatever word you want to use, I'm in favor of that!