Lady Peinforte is a woman of mystery. In some ways, she presents great contradictions. She hails from Windsor in the seventeenth century - 1638 being the precise year in which she left - but is not a woman of seventeenth-century sensibilities. She adapts quickly to new situations and thus takes twentieth-century conveniences in stride, and she even has a rudimentary knowledge of time travel. She puts her faith in science, yet is proficient in the black arts. (Unfortunately, she is not quite so proficient at archery.)
In other ways, Lady Peinforte is quite straightforward. She knows what she wants and is more than willing to kill for it. She murders for necessity and does not lament it; she even envisions her own death as merely "a door". Lady Peinforte is very single-minded about her objectives, even obsessed - sometimes to the point of insanity.
In her employ is a hardened criminal named Richard Maynarde (truly, a man of great character and noble surname!) whose reputation was no doubt tarnished by the fact that he is actually quite kind and good-hearted, if a bit misguided. Lady Peinforte does not understand why he would show her such kindness - she sees herself as utterly and irredeemably evil. Perhaps as a reflection of her feelings, Lady Peinforte likes to wear black, with just a bit of white in the lace trim on her dress.
She first met the seventh Doctor in 1638, when a quantity of metal fell from the sky onto her lawn in Windsor. This metal was validium, a "living metal" created by Omega and Rassilon as Gallifrey's ultimate weapon. Its only purpose was destruction, and therefore it was a serious concern when some of the validium got out of Gallifrey. Lady Peinforte was swift to try to use the validium to her own advantage. She formed it into a statue of herself and apparently had plans for it, but the Doctor - presumably travelling with Mel at the time - arrived and launched the statue into space, apparently while Lady Peinforte was busy fighting the Roundheads for it. But Lady Peinforte, having a nose for secrets, kept to herself a bit of knowledge that she had gleaned from the statue - the Doctor's big, dark secret. Where he came from, who he was, secrets of the Old Time - the Time of Chaos - on Gallifrey. She hoped to use these as leverage against him some day.
The statue's orbit, however, was not stable - it passed close to Earth every 25 years, getting closer and closer each time. Every time it passed, it exerted its malignant influence on the planet. Within the twentieth century alone, it caused World War One (1913), Hitler's annexation of Austria (1938) and President Kennedy's assassination (1963). In 1988, its orbit finally decayed, and the statue returned to Earth at the exact spot from which it had been launched - Lady Peinforte's ex-yard.
The statue had been made inactive by the removal of two of its components - a bow and an arrow, both made of validium, and without which the statue could not achieve critical mass to reactivate. The arrow was in Lady Peinforte's possession, and once she had learned the exact date when the Nemesis statue would return to Earth, she used the arrow in a time-travel spell to transport herself and Richard to 1988. She took with her a supply of poison-tipped gold arrows, which proved useful against a variety of adversaries.
The mere thought of possessing the Nemesis statue again sends Lady Peinforte into fits of apoplectic joy. Eventually, her focus on domination sends her over the edge, despite the fact that she has yet to obtain either the statue or the bow. Lady Peinforte becomes a bit nutty and retreats into her own little world, bragging to the unfortunates who happen to be around her that everything will one day be hers. In the end, when she is finally within reach of Nemesis and it is yanked away from her, Lady Peinforte flings herself onto the statue and merges with it, rather than letting it be taken away from her again. The statue is launched back into space, and the Doctor gives Richard a lift back to his own time.