A definition of quality is that quality is a notion of expression that is only known and recognised by an unconscious non-thinking process, and therefore since definition is a conscious thinking process, quality cannot ever be defined.
Naturally, another application of quality is as the aesthetic representation of one person to another, or of oneself. In conversation we'll employ devices such as 'he's/she's/I'm (not) nice, or (not) friendly, or (not) kind, or (not) funny, or (not) attractive, or (not) charming'. In fact, these are no more than superficial linguistic nods and winks to convey a shared sense of quality recognition with each other, and one with the also superficial presupposed subtext of 'it makes me feel good/bad'. In other words, the typical illusion of identity crap.
And, other than through good poetry, literature, music, and art, there's a lovely simple way you can at least feel personal quality through expression, and beyond the illusion of identity. It's with the wonderfully versatile suffix '-ness'. (Ignore the prescriptive grammarians who say it's only suppposed to be used with adjectives and participles - nouns are commonly used as adjectives, so it's fine.)
Your thingness is your name + '-ness'. It's the essence of you.
For me, it's my Williamness: I'm not a nothing thing and neither are you, and I want you and not some thing you have, people do things with me and not to me, any thing is possible and crossing the barriers in between is always exciting.