Dictionaries have "skillful", but as a native English speaker I feel something is missing from this definition. Am I way off in thinking of the word "alert"? Adept seems to have a sense of quickness to it, like being able to grasp things fast. That is why I think of alert.
I agree. Adept can have the connotation of agility or alertness.
This probably comes from the kind of things one is described as adept at.
"He was an adept swordsman."
"She was an adept soccer player."