Zero is considered a flat plane, in which all existence is a disturbance. These disturbances are known to Thinkamancy as G-Strings. The existence of a Unit is considered to Mathamancers as a debt, that would be repaid, eventually, by the croaking of that unit.
Several forms of magic seem to create 'debts' similar to that caused by the existence of units; debts which must be paid back to achieve balance. Luckamancy creates a debt of Numbers: the good numbers borrowed by Luckamancy must be paid back through opposing numbers. Either the side will have an equal amount of bad luck or an opposing side will have an equal amount of good luck. Carnymancy creates a debt of Fate: by rigging the rules in the favor of one unit, the rules will be rigged against another.
It is possible that Zero is the metaphysical incarnation of the Numbers Axis. By this view, G-Strings would be the incarnations of the Fate Axis, while Erfworld itself is the incarnation of the Erf Axis.
Zero might be a reference to the term "Zero Sum Game" - in game theory, it's a game where one's gains are balanced exactly by another's losses, and vice versa.