Count Olaf's mother was the mother of Count Olaf.
At some point, she gave birth to Count Olaf. Either she or her husband, or both, are from some kind of noble birth, as Olaf is called a "Count" and it is implied Olaf attended classes at Wade Academy, a prestigious school.
There is evidence that she may have been a neglectful mother, as Olaf became a sociopath/psychopath, and it is mentioned that Olaf had a hobby of burning ants with a magnifying glass as a child. However, it is unclear if this occurred because she did not monitor and care for her child enough, or if it was because she was already deceased by the time. Regardless, Olaf would become a killer in the future.
It is heavily implied (but never directly stated) that she and her husband were killed by poison dart at an opera performance of La Forza del Destino, thrown by Beatrice and Bertrand Baudelaire, with weapons provided by Kit Snicket. The motive for this is unknown.
Netflix Series Divergent Canon
She is only briefly mentioned in the TV series, as having died in a fire. Only her husband is killed by poison dart as she was deceased before the play.