The unbalanced current is the current that flows in the neutral conductor of a multiwire branch circuit or a feeder circuit due to unequal loads on the different phase conductors (or "hot" wires).Think of it this way: Balanced Load

If all the "hot" wires in a circuit are carrying the same amount of current, and those loads are purely resistive, the currents effectively cancel each other out in the neutral conductor. In a perfectly balanced three-phase system, the neutral current would be zero.

Unbalanced Load

In reality, loads are rarely perfectly balanced. When one "hot" wire has a heavier load than the others, the difference in current needs a path to return to the source. This difference flows through the neutral conductor.

In simpler terms

The unbalanced current is the current that the neutral wire has to carry because the loads on the other wires aren't using the same amount of power.

Why it matters according to the quote from 310.15(C)(1)

The National Electrical Code (NEC) section 310.15(C)(1) deals with conductor ampacity adjustment factors for conductors installed in close proximity to each other (called "raceway fill" or "cable bundling"). Too many current-carrying conductors in a bundle can cause overheating.The code makes an exception for the neutral conductor if it only carries the unbalanced current from other conductors of the same circuit. This is because the neutral carrying unbalanced current only is not carrying the full current of each of the hot wires. Therefore, it doesn't contribute as significantly to the heat buildup in the conduit or cable bundle. If the neutral is carrying harmonic currents, then it is considered a current-carrying conductor.

In essence, the rule means that if the neutral only carries the unbalanced current (and no significant harmonic currents), it doesn't have to be counted towards the number of current-carrying conductors when determining how much to derate the ampacity of the other conductors. This can allow for a smaller wire size in some installations, saving money and simplifying the wiring.

Example:

Imagine a 3-wire circuit (2 "hot" wires and a neutral) where one "hot" wire is powering a 10 amp load, and the other "hot" wire is powering a 6 amp load. The 10 amp "hot" wire is carrying 10 amps. The 6 amp "hot" wire is carrying 6 amps. The neutral conductor would carry the unbalanced current: 10 amps - 6 amps = 4 amps. This is the unbalanced current*. Flag for review