Ok, here goes: Your mom and aunt are sisters. If your mom and your aunt both had a child, those children would be first cousins. If you had a child, your child and your cousin (aunt's daughter) would be first cousins once removed. Same thing if your cousin had a child. Your cousin's child and You would be first cousins, once removed. Your child and your cousin's child would be second cousins. If your child had a child, that child (your grandchild) and your first cousin would be first cousins twice removed. Your grandchild and your cousin's child would be second cousins once removed. Your grandchild and your cousin's grandchild would be third cousins. This probably isn't making much sense... lol Think of the "first" or "second" or "third" part as meaning what generation the cousins are from. If one cousin is from one generation, and another cousin is from a different generation, then they are "removed" from each other. "once" or "twice" (etc) removed just refers to how many generations separate them. I hope I didn't make this more confusing than it has to be...

The best way to understand this is to imagine a family tree, with all the same generations on the same level. Say your paternal grandparents (dad's parents) had three children. Those children are siblings. The children of the siblings are first cousins (stated another way, your first cousins are the children of your aunts and uncles). The children of first cousins are second cousins. The children of second cousins are all third cousins, etc., etc.. The "removed" part comes in when you are describing relationships between folks from different generations on the tree. If your first cousin has a child, that child and you are first cousins once removed. If your first cousin has a grandchild, that grandchild is your first cousin twice removed. Same thing with all the other levels of cousins -- my second cousins child is my second cousin once removed (and I am the same relation to that child). The "removes" always count steps away from the primary cousin relationship, be that first, second, fifteenth, whatever. Make sense?

A second cousin can be the child of your FIRST cousin, who is the son or daughter of your Aunt or Uncle, whichever is one of you parents siblings. Once or twice removed could be the child of a second cousin. I know, Clear as Mud.

First of all, imagine your family tree as 'steps', you can go up one step, to your parents, two to your grandparents, three to your great grandparents and so on. You can then also come down in the same way, one 'step' for each generation. Remember your cousins (or first, fith or 100th cousins) have parallel family trees that move up and down in step like yours. The second cousin bit, means that you have to go further up your family tree to get over to their family line. So your cousins are your PARENTS siblings children, your second cousins are your GRANDPARENTS siblings grandchildren. For every step you go up (third cousin, fourth cousin etc) you go one step further up the family tree, before you move over to their siblings and back down however many steps you went up. The second part (the twice removed part) indicates that the generations are displaced, therefore, if you go up 3 steps up your family tree before you move over to their siblings (your 3rd cousins) then for the 'twice removed' part, you only come down 1 step (so your great grandparents siblings children) or down 5 steps (so your great grandparents siblings great great great grandchildren) so the people in question are 2 generations away from you.

Your second cousin is a person with which you share a pair of great-grandparents (vs. for example your first cousins, with which you share a pair of grandparents). Your "second cousin once removed" is the parent or child of this person, as they are "removed" by a generation.

Your mother or father's second cousin is your second cousin once removed. Their children would be you third cousins. Removed indicates a generation gap between you and the relative. Once means one generation. First. second, third indicate how far back you have to go to reach the common ancestor (excluding parents). First cousins are one step (grand-parents), second cousins are two steps (great-grandparents), etc.