There are many ways to perceive balance of trade between countries. One perspective that can be useful is to consider the process of equilibrium. In biological systems the process of homeostasis, for example, denotes the continuous fine tuned adjustment around a desired point of equilibrium. This balance is achieved by constant monitoring and adjustment of the internal environment.
This process of finding balance is an useful perspective for considering economic action.
The fact is that value is based on perception on the individual level, and the aggregate of all such judgments in an area establishes the value of any one thing.
Balance of trade may be considered as the point at which the population groups in two clearly defined areas reach a common perception as to the value of all goods.
Note that I am not even bringing the monetary plane into this discussion; simply the aggregate value judgments of all players in the defined regions.
Once there is a general agreement on the value of any one good , i.e. when considering balance of trade between two zones, no party values the good more than the other, then flow of that good ceases, and value judgments are in sync.
It goes without saying that this perspective is not that relevant in our current economic paradigm. However once we enter a FreeGold paradigm, it is a useful view for understanding how balance of trade will occur.
Once agreement is reached on all possible goods flowing between zones, trade is balanced. It should be noted that such stasis is only a temporary condition, as the needs, wants and positions of the individuals involved continue to change, altering the point of equilibrium that needs to be reached, and is strived towards.