Interpretation with partial correlation

#1
Hello everyone!

I have a general question that is not related to any specific study of mine but that I was just wondering about in general.
What does it mean if the correlation coefficient between two variables X and Y increases after controlling for a third variable Z?
My suggestion is that including Variable Z can "improve" the association between X and Y. However, how exactly does that increase happen? Does Z have a positive relationship with X and a negative relationship with Y?

Thank you very much for your help!

All the best,
Helena