It means they are one generation removed from you on your family tree. Your second cousin once removed is either your parent's second cousin, or your second cousin's child.
The son of your second cousin is your second cousin, once removed. You are also his second cousin, once removed.
Your parent's first cousin is your first cousin, once removed. Your parent's first cousin, once removed is your first cousin, twice removed. Your parent's second cousin is your second cousin, once removed. Your parent's second cousin, once removed is your second cousin, twice removed.
Your second cousin's son (or daughter) is your second cousin, once removed.
Your mother's first cousin is your first cousin, once removed.Your mother's first cousin, once removed is your second cousin.Your mother's second cousin is your second cousin, once removed.
Your parent's first cousin is your first cousin, once removed. Your parent's second cousin is your second cousin, once removed. Your parent's first cousin once removed may be your second cousin.
If your first cousin has a child, you and that child are first cousins, once removed, to each other. If your second cousin has a child, you and that child are second cousins, once removed, to each other.
One of your second cousin's parents is your first cousin once removed.
Your first cousin's child is your first cousin's, once removed. Your second cousin's child is your second cousin, once removed. Your third cousin's child is your third cousin, once removed.
Your first cousin's father is your uncle. Your second cousin's father is your first cousin, once removed - or the husband of your first cousin, once removed. Your third cousin's father is your second cousin, once removed - or the husband f your second cousin, once removed.
Your 1st cousin's child is your 1st cousin once removed. Your 2nd cousin's child is your 2nd cousin once removed. And so on...
The son of your second cousin is your second cousin, once removed. You are also his second cousin, once removed.
Your mother's second cousin twice removed is either your third cousin once removed or your second cousin three times removed. Which it is depends on whether the second cousin twice removed is the grandchild of your mother's second cousin or the grandparent of her fourth cousin.