What does it mean for a joint distribution to be separable?

Given the joint distribution of two image-pixels at an offset v from each other modeled as

$Y(x_1, x_2; v) = Prob(f(u)=x_1 $ and $ f(u+v)=x_2)$

what does it mean to say that the joint distribution is not separable for any $v$?

This may be more of a general question of separable joint distributions, but I am guessing that it’s related to the function and whether it is separable? Can anyone provide examples of this? I’m finding it difficult to find answers elsewhere that aren’t muddled with a lot of irrelevant subject matter to weed through.