I like this explanation the best:
What does "cousin once removed" mean?
The relationships to your cousins can see a bit confusing. You will undoubtably uncover second cousins and third cousins and then sometimes they will be "once removed" or "twice removed". But what does all that mean?
Firstly a cousin is someone with whom you share a common ancestor. My first cousin and I share the same grandparents. They are our common ancestors. My second cousin and I share the same great-grandparents - our common ancestors are a generation further back.
The word "removed" means that the cousins come from different generations. "once removed" means that they are one generation apart, "twice removed" means that they are two generations apart, and so on.
Here's an example:
My first cousin's child is my first cousin once removed. My first cousin's grandchild is my first cousin twice removed.
However my child and my first cousin's child are second cousins. They are of the same generation, hence they are not "removed", but their common ancestors are their great-grandparents which is why they are second cousins.
Source:
http://www.certificate-exchange.co.uk/family-tree-articles/c...