So, what does your statement mean in terms of negative and positive lags?

For example if you have two series X and Y with n points each(i.e X(1),X(2)...X(n); Y(1),Y(2)...Y(n)). Then lag 0 is the simple correlation.

Lag1 ccf is correlation between..{X(2),X(3),...X(n)} and { Y(1),Y(2)...Y(n-1)}

Similarly lag -1 would be correlation between {X(1),X(2),....X(n-1)} and {Y(2),Y(3),....Y(n)}

I have attached an illustration. Hope it helps!