Quietism has several definitions. Used most broadly it refers to any spiritual system that emphasizes or demands silence in a religious context. Thus in a strict quietist meeting there would not be any sermon, singing, discussion or vocal prayer. God would be heard inwardly and privately. It’s unlikely that any such group ever existed, or if it did exist then it didn’t exist for long.
Elements of quietist practice have moved throughout Christianity however. The most widespread of these modified quietist movements was in the 17th century and is associated with Catholic names such as Jean Guyon (also known as Madam Guyon), Michael Molinos and Fenelon. The basic idea of this movement was that Jesus could be found inwardly and therefore a Christian should be less dependent on the clergy, the liturgy of the Church, preaching and fellowship. As you can imagine, this resulted in a fair amount of persecution from Organized Religion.
A related movement is pietism. This refers to an inward spiritual formation that stresses holiness, spiritual disciplines and prayer.
The best known Protestant proponent of quietism/pietism practices was George Fox and what became known as the Quakers. He taught that an inner light, from God in the person of the Holy Spirit, was available to any Christian and would guide and teach the believer. There was some opposition to this movement from other Christians but in America the movement grew and prospered.
Several errors and heresies have been associated with Quietist theory and practice. The most serious charge is that Quietists believe that since they are finding God inwardly they can become entirely spiritual beings. Thus their bodies are not really “their true selves” and consequently they are not responsible for bodily actions and they are therefore free to act in any way they want. Most famously then they are free to engage in immoral sexual behaviors. It isn’t clear from the historical accounts how many Quietists actually believed this heresy. Michael Molinos is accused of teaching this absurd doctrine but a study of his teachings fails to reveal such an error. Certainly the Quakers did not teach or practice such a doctrine. Lesser charges revolve around the fact that Quietism minimizes Church authority and the need for community and fellowship. These are indeed dangers inherent in an inward approach to God, and those of us that believe in Quietist/Pietist claims need stay grounded in the written Word of God and in the Body of Christ.