In the actual reality game, feeling busy is often a sign of a failure of strategy. Most often, I think, busyness is a signal of the absence of a viable strategy for the game. Without a strategy, each new event, each new question, each opportunity, each chance encounter stands at the same level and demands the same amount of attention. The truth is that not everything that comes up requires an immediate response, or any response at all in some cases. With a solid strategy, it is possible to differentiate between occurences which demand immediate attention, those which require a tactical response, and those others which can be allowed to pass by without a reaction.
Without such a strategy, it is hard to find enough time to deal with even the most urgent matters. With a good strategy, time, attention, and resources can be put into play in a rational way. The urgent matters are disposed of and time is available for the more pleasant pursuits.
There is a more positive sense of "being busy". Even on a vacation or when retired, most of us prefer to "keep busy". We want to be active both mentally and physically. Some people may accomplish that with a tightly planned and structured type of play ("on my vacation I will read the following four masterpieces of philosophy in their original language and run 3 miles at 7:00 a.m. and at 6:35 p.m.") but most of us prefer to let the life around us set some part of our daily agenda. This is an intentional sort of busyness and we manage it by setting the level at which the mundane may intrude into our consciousness.
The extreme of busyness is distraction by every singing bird and drifting cloud, every truck shifting gears and passing stranger. The opposite extreme is obliviousness. The middle ground is long and broad and allows much room to maneuver.