What is the relationship between you and your cousin's daughter or son?

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I assume that you are asking what we would call the way that I would be related to such a person.  I also assume that you are asking about the daughters or sons of my own first cousins.  If these assumptions are correct, the answer to your question is that these people would be my first cousins once removed.

We are all familiar with the concept of first cousins.  These are people who have different parents than us, but who share a set of grandparents.  Put differently, these are the children of our parents’ siblings.  We are of the same generation as our first cousins since we are both two generations away from our grandparents.

However, when our first cousins have children, we and they (the children) are not of the same generation.  Instead, we are two generations away from our common ancestor while the children are three generations away.  Our grandparents are their great-grandparents.  Therefore, we call them our first cousins once removed because they are “removed” from us by one generation.

If we also have children of our own, they become the second cousins of our first cousins’ children.  So, if my first cousin and I each have offspring, my offspring and hers are second cousins while my offspring and my cousin (and her offspring and I) are first cousins once removed.

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