Nuance: n. a subtle difference in color, meaning, tone; a shade, a gradation. From the French nuer, to show light and shade; originally from Latin nubes, a cloud
If you were old-fashioned enough to want to be guided in your English usage by the venerable H.H.Fowler, he of Fowler’s Modern English Usage, you might see the use of “nuance” as breaching his admonition to “prefer the Saxon word to the Romance”. Except that, as far as I know, there is no single “Saxon” word that does what “nuance” does.
In any case, a companion admonition of Fowler’s is “prefer the single word to the circumlocution”, by which standard, “nuance” serves better than, say, “a subtle difference in meaning”, “a gradation of color”, and so on.
Pronunciation varies from something like the French, with the first syllable as in “noo”, or in a more Anglicized way as in “new”.
How might I use the word?
One thing I hope I would not do is use a phrase like “subtle nuance”, which would be a tautology, given the “nuance” already contains the meaning of “subtle”.
Thinking about that derivation from the Latin for “cloud”, via the French for “to show light and shade” I would use it in sentences such as the following:
“I listened to both speakers explain the new arrangements and with the second speaker I thought I detected a nuance that these new arrangements would be regarded as strict rules, not just as guidelines.”
“It was supposed to be a curry, which for me would mean that it would be spicy, not bland, but there was only a nuance of some spice I could not identify.”