Balanced is one of the most abused and misused words in hifi.
The main benefit for a balanced connection it help feed a quality signal over longer distances. Yes
And also makes sure the signals reach the speaker or headphone cup (diaphragm) at the same time(?), for better imaging(sound stage?). No
An un-balanced connection is one signal channel and one ground channel, per speaker or headphone cup (diaphragm) Sorta
A balanced connection is two signal channels, with one (or two?) grounding channel(s), per speaker or headphone cup. Not quite
Headphone cables are usually a short distance, so I'm assuming a headphone with balanced connection helps with imaging (sound stage?) No
And I guess a balanced connection helps reduce interface (another guess). Sorta
Ok here's the super condensed version that ignores some details/technical matters.
Unbalanced (aka single ended in this scenario): You have one signal wire. Your reference point is ground (zero volts for all intents and purposes). Your output (headphone or speaker) is the voltage difference between the signal and ground.
Balanced: You have two signal wires. There is a ground, but you don't use it directly. Your output is the difference between the two signal wires. Typically the signal in these two wires are inverted from each other, but not necessarily. One of the wires could simply be zero volts, which also works. Just because that wire is zero does not mean it is ground. If that doesn't make sense, don't worry about it.
Unbalanced: if you have crap/noise/interference in a signal wire, and you take the difference to ground, then you get that crap on your output.
Balanced: If you have equal crap on both signal wires, then taking the difference cancels out the crap. Awesome, except it only cancels if both wires are perfectly balanced and implemented correctly, otherwise you've just doubled your device cost and complexity for no reason.
A well done unbalanced system can sound great. A poorly done balanced system will not.