Broadly speaking, a purgatorial society is any association of Catholic laypeople, religious, and/or priests who work together to assist the poor souls in Purgatory. Through prayers for the dead, Masses for the dead, and other acts of charity, the members of purgatorial societies attempt to receive indulgences applicable to the souls in Purgatory, thus reducing their time in Purgatory and hastening their entrance into Heaven.
In the Middle Ages, purgatorial societies were very popular, and entire religious orders were devoted to relieving the suffering of the poor souls in Purgatory. But with the Protestant Reformation and the attack of the reformers on the doctrine of Purgatory, interest in the purgatorial society began to wane.
In recent years, however, some parishes have begun to revive the purgatorial society for the members of the parish. This usually takes the form of a series of Masses (often ten) offered in November, the month of the Holy Souls in Purgatory. Parish members enroll their faithful departed, friends and family, in the purgatorial society, and those names are placed on the altar when the Masses are offered.
Catholic laypeople have created more informal purgatorial societies, in which the members offer Mass intentions and prayers for the faithful departed enrolled in the purgatorial society. Here at the About.com Catholicism GuideSite, we have our own purgatorial society, and you are invited to enroll your departed friends and family in the About.com Catholicism Purgatorial Society, and to pray for all of the dead enrolled therein. (Simply offer the prayers "for those enrolled in the About.com Catholicism Purgatorial Society.")
Please also consider having your parish priest offer Masses for the About.com Catholicism Purgatorial Society. (Simply list the Mass intention as "The About.com Catholicism Purgatorial Society.") And if you are a priest who is willing to offer Masses for those enrolled in the About.com Purgatorial Society, please e-mail me your name and your parish affiliation, and I will list you on the About.com Catholicism Purgatorial Society page.