I don't know why, but despite having read the definition over too many times to count, its one of those words that just doesn't click. I see it being used in sentences and have never been able to fully understand it either. Could someone help explain it, and use it in a sentence? Thanks!
WS2's answer provides the definition and offers appropriate examples, but perhaps some further explanation might give some insight into how "nuance" is used.
Two singers might sing exactly the same words to exactly the same tune using exactly the same tempo. But if one singer adds some extra depth - perhaps by a slight hesitation before a critical word, or singing certain words louder or softer than usual - then this would be described as adding nuance, or their performance was nuanced.
A key element of nuance is its subtlety: in other words, it's only by careful observance that the full meaning becomes apparent. Another element is that nuance can only be fully appreciated (or in some cases, even understood at all) by someone with experience or knowledge of that particular matter.
Great actors bring nuance to the lines they speak. A fine example is Ian McKellen's rendition of Macbeth, and in particular his final soliloquy "Tomorrow and tomorrow and tomorrow". See here for McKellen's explanation for the nuance he brings to the performance of this memorable speech. This might give further nuance to your understanding of the word.
Nuance, meaning a subtle difference in shade of meaning, expression or sound exists as both a noun and a verb. An example of its use as a noun would be:
He was familiar with the nuances of the local dialect
And as a verb:
The effect of the music is nuanced by the social situation of listeners.
Meaning and examples taken from Oxford Dictionaries Online.