The news that we learn about Rebecca Nurse is that she has been accused of witchcraft.
Specifically, we learn that she has been deemed responsible for the deaths of Ann Putnam's children. Ann, deranged by the loss of so many children in infancy, is convinced that Rebecca, an elderly lady well respected in the community, has deliberately killed her offspring by casting some sort of malevolent magic spell.
This accusation isn't true, of course, but given the feverish level of hysteria gripping Salem, it becomes widely believed, and Rebecca is arrested for witchcraft. Later on, in act 3, we find out that she has been convicted on the strength of the “evidence” put forward by Abigail and the other girls.
That such a good, devout, and respected woman is convicted of witchcraft is a sign of how rapidly the Salem witch hunt is getting out of hand. If someone like Rebecca can fall victim to the collective hysteria—and on the flimsiest of evidence—then anyone can. No one is safe.