"Nuances" are very small differences between things. A good example of this is a person's facial expressions. When someone is happy, they smile. But people also smile when they're nervous. The difference between the two kinds of smiles is an example of a "nuance".
The meaning of "subtle" is very similar to "nuance", but "subtle" is an adjective. So when you put together "subtle" and "nuance", it means really, really small differences between things.
So what can kinds of situations do you talk about "subtle nuances" in? This phrase is useful for talking about communication, ideas, art, and so on:
There was a subtle nuance in the way that she said it that made me think that something was wrong.
Our English teacher does a really good job of explaining the subtle nuances between words.
Looking at a painting in person is a totally different experience. You're able to pick up on lots of subtle nuances in the color, the brush strokes, and so on.