Interesting that most of the answers went technical with this. My first thought was psychological. In addition to the “activity” itself, of which there are limitless types, there is the complexity of mind over matter – encouraging the clint, or helping the client to motivate him or herself to engage in the activity in the first place. I see that as a set of developed skills at least equally important as the activity undertaken.
Physical activity is movement of the body; on a cellular level there are certainly numerous, relatively complex things that must occur, for instance, for a single muscle contraction.
I think the description/definition above might be more applicable to “exercise”: because this is a more structured, pre-planned activity that requires systems and strategies for it to occur successfully on a consistently regular basis.