When the correlation b/w A and B is 0, they are uncorrelated, but not necessarily independent in between. This is because the correlation coefficient detects ONLY LINEAR dependencies, i.e. correlations.

As an example, imagine X being constant of 3 and Y = X^2 for any given X. Clearly, Y is correlated to X. However, as there is NOT ANY linearity b/w the two variables, their CC = 0.

Hope this have been clear to you.