Mrs. Putnam makes this statement in reference to the fact that she has lost seven out of eight babies within a day of their birth. She and her husband have sought answers, have prayed about it, but to no avail. The Putnams and Rebecca Nurse are discussing what Rebecca calls the "prodigious danger in the seeking of loose spirits" as a result of Mrs. Putnam's admission that she sent her only surviving daughter, Ruth, to Reverend Parris's Barbadian slave, Tituba, to conjure the spirits of Ruth's dead siblings in an effort to learn what caused them to die.
When Rebecca suggests that the community must look to themselves for the cause of such deaths, Mr. Putnam says, "I am one of nine sons; the Putnam seed have peopled this province. And yet I have but one child left of eight! -- and now she shrivels!" Mrs. Putnam questions Rebecca as to whether she believes it is God's work that Rebecca would never lose a child or grandchild, and yet the Putnams have lost all but one. Mrs. Putnam clearly believes that this is not God's work -- why would God punish her so cruelly? -- and so it must be the Devil's.
When she then says that "There are wheels within wheels in this village, and fires within fires!" what she means is that there are secrets at work, conspiracies and plots among those townsfolk who are in league with the Devil and who do his work for him. When Tituba names Goody Osburn as a witch at the end of Act One, this confirms all Mrs. Putnam's suspicions. She says, "I knew it! Goody Osburn were midwife to me three times [....]. My babies always shriveled in her hands!" It is easy to believe because Mrs. Putnam wants so badly to believe it. She wants there to be an answer to her question, and this would seem to be one.