We all know what a cousin is, the child of an aunt or uncle. This is also called a first cousin.
The "removed" part refers to a different generation. For example your first cousin's child is your first cousin once removed (in genealogy shorthand 1C1R).
In the tree below
Margaret and Marion McFedries are sisters, daughters of David McFedries
Their children are Isabella Campbell and Hugh Fleming (first cousins), they share grandparents.
The row below Marion M M Patrick and Isabella M Fleming are second cousins, they share great grandparents.
And Mary W McMeekin is a second cousin once removed to Marion M M Patrick.
Back to the first cousins, if Margaret and Marion McFedries had different mothers, they would be half sisters and their descendants would be half cousins and so on as well.
In this second tree
Alexander Anderson (the poet) is a first cousin of James Anderson born 1828, so all of James Anderson's children will be first cousins of Alexander, you just need to count the generations to get the right degree of removal. Jane Anderson Reid is a first cousin three times removed (1C3R).
