One of the most confusing things you will encounter in your quest to list all of your ancestors in your family history is trying to figure out their relationship to you.
I find that the relationship calculator from Ancestry.com does an excellent job of mapping out how a specific person is related to you. This is quite easy to do - all you have to do is click on the person's relationship information found directly below their name on the main page for that person and voila, you have an instant mini tree that shows how the two of you are related.
However, you may still have no idea how a specific person becomes your 3rd cousin 3 times removed, or what it means. In order to simplify the relationship calculation between relatives, here is a simple means to calculate:
First Cousin - these are people in your family with whom you share a common pair of grandparents.
Second Cousin - these people have the same great-grandparents as you, but not the same grandparents.
Third Cousin - these people have the same great-great grandparents as you.
To further complicate matters, you will often see the term "removed" added in when it comes to calculating your cousin relationships. What does "removed" mean?
Once Removed - this means that there is a difference of one generation between you and your cousin. Your parent's first cousin would also be your first cousin, but 1 time removed as there is a difference of 1 generation between you and your parent.
Twice Removed - this means that there is a difference of two generations between you and your cousin. Your grandparent's first cousin would also be your first cousin, but 2 times removed as there is a difference of 2 generations between you and your grandparent.
So, going back to the original question, what is a 3rd cousin, 3 times removed? That person would be a cousin who shares the same great-grandparents as you do, but there is a 3 generation difference between the two of you.
There are calculators that you can use that will automatically calculate your family relationships, but a basic understanding of cousins will help you better understand where to look for a common ancestor. This can be especially helpful when trying to track down a common ancestor when you find matches using DNA testing.