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The tautological answer to the question "what is the centroid $x_C$ of $C$?" is "the centroid $x_C$ of $C$ is the centroid $x_C$ of $C$". It is hardly possible to give a better answer to this question without having the terms in which to express $x_C$ specified.

The answer to your second question, "How is it related to $x_A+x_B$?" is "in no reasonable way". For instance, it should be easy to find two compact convex subsets $A$ and $B$ of $\mathbb{R}^n$ with $x_A=x_B=0$ but with $x_C=x_{A+B}$ being any prescribed vector in $\Bbb R^n$.