Mrs. Putnam has been completely unhinged by the loss of her infant children. She's as devout a Puritan as anyone in Salem, and yet she still hasn't been blessed with a child; all her babies have died within a day of being born. Mrs. Putnam cannot believe that this is God's work; after all, her husband is one of nine sons. So she figures that there are dark forces at work; the Devil is responsible for her loss.
But the Devil can't work alone; he needs human helpers. Mrs. Putnam gets it into her head that there must be a gigantic conspiracy between the Prince of Darkness and some of the supposedly God-fearing folk of Salem. That's what she means when she says "There are wheels within wheels in this village, and fires within fires!" She's emphasizing how Satan's accomplices are hiding in plain sight, masquerading as godly Puritans, when in actual fact they're actively in league with the Devil.