So what does balance mean? What does it focus on?
Balance implies well-roundedness -- experience in lots of areas, not overly developed in any one area or any one discipline.
The advantages of balance in the sense of well-roundedness are equilibrium and synergy.
Having exposure to lots of areas and disciplines and functions means there are more opportunities to develop diverse and stabilizing networks of people and experiences. Knowing a lot of people and knowing about a lot of things can create a healthy sense of perspective and purpose. One is less apt to be carried away on some emotional or intellectual jag and more apt to be able to weigh the benefits and costs of different decisions and paths.
On the other hand, lacking extraordinary development in one area could mean under achievement, at least compared to persons who focus on one interest or one area rather than many. At its poorest, this is the "Jack-of-All-Trades-Master-of-None" dilemma. When it seems that everyone else is investing most of their time in their "passion," spending time pursuing multiple interests may put one at a relative disadvantage.
The key, perhaps, is not a narrow monotony of interests, fixated on one or a few things to the point that one's vocabulary and communication and range of behavior has been truncated, not expanded. Few understand the arcane language of the narrow expert, and fewer still care. Rather than this kind of reductive approach, one seeks a challenging attack on multiple areas of interest and action, a fuller expression of one's personality and character.
To be sure, there are reasonable limits on the number of interests and activities one can productively pursue. Plainly, there must be some ... balance ... between the number of interests one pursues and time spent in any one area.
Assuming some healthy respect for limits, insights gained in one discipline or area of interest can enhance one's exploration of other disciplines or areas of interest. So a well-rounded person with multiple interests, within reason, is not necessarily falling behind someone else or sacrificing depth for breadth. Indeed, some say creativity often involves combining different, evenly wildly different, points of view or thoughts into a new idea. See, e.g., Frans Johansson, The Medici Effect.
The ancient concept of balance conveyed this sense of wholeness and health. Plato and Aristotle write of the "golden mean" while Buddishts speak of the "middle way." Again, this is not to be understood as middling mediocrity but, instead, a vigorous pursuit of excellence in all things.