Ow. It's not that easy to present an in-depth analysis or synthesis of Moral Contextualism (MC for short), when it is a fairly recent development of moral philosophy, and the relevant online literature is available only through a paid subscription. The first (and, to my knowledge, only) international conference specifically dedicated to MC was staged at the University of Aberdeen in 2006 (see here for details.) It doesn't bode well for the rest of this article :-/

MC is an offshot of Epistemic (or Epistemological) Contextualism (EC) which focuses on moral issues (obviously.) You can find general articles on EC on both the IEP and the SEP, and, of course, Wikipedia. To make it short, at the risk of being simplistic, I'd say that Moral Contextualism is born from some moral philosophers' dissatisfaction with Moral Relativism (while opposing Moral Absolutism.)

The discussions and commentaries I've seen so far on this topic are quite technical, with a strong bent towards semantics and information theory. Surprisingly (or maybe not), when I tried to remove most of the jargon and interpret the rest, there was little meat left (I may be responsible for this, I tend to be heavy-handed with cleavers.) So, what I could gather so far about MC, in everyday terms, can be summarized as:

(1) Moral judgments involving qualifiers such as 'good', 'moral', 'appropriate', 'acceptable', etc. are context-dependent.

(2) What varies from context to context are the moral standards that an action or conduct must match to be considered 'good', etc. In most contexts, these standards are low enough to be easily satisfied, but they may be raised when the action or conduct is performed in a controversial context (Hum, I have to say I'm a bit baffled by this, it smells a lot like circular reasoning to me.)

(3) However, it doesn't mean that morality is necessarily subjective: on the contrary, there are unambiguous cases where certain actions are objectively right or wrong.

(4) Moral judgments could be said to be analogous to ascriptions of physical properties such as brightness or bigness. E.g., the truth value of a statement like 'Fido is a big dog' is not directly assessable. Plus, it might just mean that Fido is big for a dog its breed and age. A statement like 'What Mary did is good' should be evaluated in a similar way.

(5) Did I get all the above right? I'm not so sure. Is it sketchy? Certainly. Blame Adriana, she's a tyrant. I should never have let her lure me into writing this.