From my perspective, this quote is about mindfulness. Paying attention. Focusing on what I'm doing right now.
"Still in the midst of activity" happens for me when I'm absorbed in what I'm doing. An example would be drawing a barn quilt pattern or crocheting or even golfing. I'm completely into the activity and not thinking about other things, like what I'm going to do next. This becomes a challenge when I'm doing something mundane like washing dishes. It's easy to let the mind wander and not pay attention to the dish, the ability to wash it, and the resources (warm water, soap, sink) to do it. See--you don't think about that stuff when doing the dishes, do you? Tasks like that can become an annoyance rather than an opportunity to recognize the routine blessings of life.
"Vibrantly alive in repose"... hmmm... When I'm relaxing, not doing anything, this is the time to be most aware of myself, my thoughts, my internal state. Open to the divinity within me, paying attention to that "still, small voice" within. "Vibrantly alive" means maintaining and sending out a positive vibration, which I seek to do most of the time. As a yoga instructor, I think of savasana at the end of the practice, wherein one lies still for a few minutes, vibrantly alive in repose, energized from the practice. I feel vibrantly alive yet very peaceful. It's a precious time to focus within.