Tonality is the overall character created by a system's frequency balance — the relationship between bass, midrange, and treble, and whether the pitch and timbre of notes come out correct relative to one another across the audible range. Tonal balance is the narrower phrase for the balance between those regions: too much low end and things sound leaden and dull; too much top and they sound bright and potentially harsh. Getting this balance right is the single biggest factor in whether a headphone sounds natural — and, for most listeners, the biggest factor in whether they actually enjoy it.
The reason the word feels like it connects everything is that it does. A startling number of perceived qualities trace straight back to tonality. Warmth, brightness, darkness are tonality almost by definition. Note weight — thin versus thick — is mostly the lower-midrange and mid-bass balance. Perceived detail is heavily shaped by treble balance and by masking. Shoutiness, sibilance, harshness are specific regions of the balance pushed too hard. Even soundstage and openness are nudged by midrange balance. Most common sound-signature words are, underneath, tonal-balance words.
This is why the field organizes itself around what the reviewer Crinacle popularized as the tonal–technical dichotomy: tonality on one side (the frequency domain — the balance), technical performance on the other (resolution, dynamics, staging, transients — how well). A subtlety in his own approach is worth borrowing: he judges tonality not purely by deviation from a target curve but by how well a transducer executes the signature it's going for. A well-done warm-V tuning can score well on its own terms; a botched neutral attempt can score badly. He tries to be signature-agnostic about it.
Closely related is timbre — the tonal character that lets you tell a violin from a viola, or a real piano from a synthesized one. Timbre is what's at stake when reviewers say an instrument sounds off, plasticky, or metallic; it's tonality at the level of individual instruments, and it's largely, though not entirely, a product of frequency response. When the broad balance is wrong, timbre is usually the first casualty.
The genuinely hard problem is neutral. Consensus says it means no region over- or under-emphasized — bass neither bloated nor anemic, treble present but not prominent. But neutral is famously reference-dependent: people calibrate it to the closest-to-neutral thing they've personally heard, so to one listener it skews slightly bright and to another slightly warm. Target curves like Harman and diffuse-field are formal attempts to pin it down, and they help, but no curve ends the argument — partly because a headphone that measures flat doesn't sound flat. You actually need a boost around 3 kHz to sound neutral on a headphone, among other quirks of how we hear them.
The practical upshot is that tonality usually matters more than any isolated technicality. A headphone can have superb separation, resolution, and dynamics, but if its tonality makes vocals sound like they're trapped in a metal tube, it will still sound wrong; a modestly technical headphone with excellent tonality can be far more enjoyable for actual music. When a reviewer praises a headphone's tonality, they mean voices and instruments sound believable and the whole response hangs together — the foundation everything else is built on.