What does it mean having a relative that is "removed?" An example would be helpful in the description. Thanks!

...Refers to the relation of different generations of descendants of first cousins to each other.

Children of siblings (let's call them "Adam" and "Eve") would be first cousins.
Let's call these cousins "Jane" and "John."

Jane's and John's children would be second cousins to each other. (Let's call them Mary - Jane's child - and Tom - John's child.)

Mary's and Tom's children (Kate and Bill respectively) would be third cousins to each other.

Each generation is one step down from original first cousins Adam and Eve -
This is where the removed part comes in!

Jane and John are first cousins to each other, but are first cousins once-removed to each other's children, Mary and Tom.

Mary and Tom are second cousins, but are second cousins once-removed to each other's children, Kate and Bill.

Now - Jane and John, the first cousins, are first cousins twice-removed to each other's grandchildren, Kate and Bill.

Now - Mary and Tom are second cousins, but are second cousins once-removed to each other's children, Kate and Bill.
Mary and Tom would be second cousins twice-removed to each other's grandchildren.

Clear as mud?

These are a couple of websites that may help if I didn't :

http://www.genealogy.com/genealogy/16_cousn.html?Welcome=1035135855

http://www.janyce.com/gene/cousins.htm

That was a perfect example!