What is meant by, e.g. '6th cousin twice removed'?

A couple of external links that may help

http://www.searchforancestors.com/utility/relationshipterms.html

http://1.bp.blogspot.com/-zp5J0kzU4kE/Tu0AbnwPOtI/AAAAAAAABD8/-ueVI...

It means that you share a common ancestor, but the distance between you and that ancestor is not the same distance between Sharon and that common ancestor.

http://www.wikitree.com/articles/relationships.html
http://en.wikipedia.org/wiki/Cousin

6th cousin means that at 7 generations back your ancestor was a brother or sister of another person..So at 6 generations down, you would be 1st cousins..But as each cousin generation continues down, it is said to be at a remove..So the 1st generation's cousin's children would be classed as once removed..Their children's children, twice removed, & so on....It is easier to draw this in a tree, but I hope you get the picture?

Hi Erica, Jonathan and Danielle! Thanks for your replies - two from the USA and one from England! I never expected this! And, what's more astonishing is that all three of you are related to me - and we would be related to each other! So, hi 'cuzzins'! :-) Erica is my 19th cousin 4 times removed; Jonathan is my 19th cousin 5 times removed and Danielle is my 6th cousin once removed. Thanks for the links - I will try to figure out how it 'works'! I reckon I can understand why Danielle and I are 6th cousins once removed. Our pivotal connections are Martha Du Plessis (my 4th g-grandmother or 5th grandmother), and Pieter du Plessis (Danielle's 6th grandfather or 5th g-grandfather). Martha and Pieter were sister and brother. Or do we have to go back to Martha and Pieter's father and work from there? He would be our most recent common ancestor.
To refer to Jonathan's comment: The distance between myself and the common ancestor is shorter than the distance between Danielle and our common ancestor. (By one? Is that what 'once removed' means, or is the fact that we are dealing with a brother and sister 'the once removed', i.e. the distance between the brother and sister?). Maybe I will understand all of this better once I have read the articles!

Thanks - I have read the four articles now! I'm still a complete 'layman' on these matters, but I now know where to look for answers. I understand the 'easier stuff', but I struggle with the more distant relationships! I will rely on Geni.com! :-)