Margaret, who has become popular in recent years thanks to the books of Philippa Gregory, was one of the most important late medieval women. It was through Margaret, a descendant of Edward III through his third son, John of Gaunt, that Henry VII claimed the throne. Margaret's actual eligibility to the throne was doubtful, given that she was descended from John of Gaunt's third marriage, to Katherine Swynford, which occurred many years after the couples' children were born. In spite of this, Henry, who spent most of his early life in exile in Brittany, was able to present himself as a credible candidate to the throne in 1485, thanks largely to the efforts of his mother.
Margaret Beaufort was, by far and away, the most powerful woman at the early Tudor court, provocatively signing herself as 'Margaret R' - playing on the ambiguity of the letter 'R' (did she mean Margaret Richmond or Margaret Regina?). She completely overshadowed Henry's queen, Elizabeth of York, and the queen dowager, Elizabeth Woodville, even being called upon to administer justice on an official basis in the midlands.
I wrote a biography of Margaret a few years ago (Margaret Beaufort, Amberley 2010) and must say that she was one of the most fascinating subjects that I have written about. Her life was filled with high drama, with Margaret herself believing that she was governed by the random turns of Fortune's Wheel.