"Third Order" signifies a lay member of a Christian religious order; that is, a person who wishes to be a member of a religious order and follow certain rules and lifestyle options, but does not live in a monastery or nunnery. Even today, people who fall into this category—sharing in the spirit of a religious order but living a secular life—can be found in Roman Catholicism, Lutheranism, and Anglicanism.
Originally, these tertiaries (Latin tertiarii, "third") began in the 12th century. If there is a third, then what are the first and second? First denotes the male order, since the male monastic version was usually the first founded. Second was when women wished to participate in the same order. For example: St. Francis, after being credited with establishing the Friars Minor, then established the Poor Clares, and afterward the Third Order of St. Francis. The Rule of the Third Order of St. Francis has become the standard for other third orders.
Those wishing to follow a third order often gathered in communities, called confraternities. There exists a Durham Liber Vitae, the Durham "Book of Lives," which is a confraternity book with a list of about 20,000 names (from the 9th century to about 1300) of those who were visited and supported the church in Durham. Donors to churches were often called confraters, a nice honorary title in exchange for their patronage. Groups like the Templars also had systems by which lay people could be confraters and support their mission.
The Second Vatican Council codified the "lay vocation" of the third orders, distinguishing it from a consecrated state. The various third orders had to revise their rules and submit them to the Vatican for approval. The term "third order" began to be replace by "secular order" to indicate that they were living "in the world" as opposed to cloistered.
An example of a third order religious who was active and influential in the secular world was Catherine of Siena, briefly mentioned here but sorely deserving of more attention, which I will give her next time. Until then...