Third orders were begun initially in the Middle Ages when the monastic movement mushroomed and the monk was the Christian ideal. Therefore, it was natural that devout laity (the first use of this word appears to be in the first century by Clement of Rome) felt the need to imitate monks and nuns.
Maybe the attitude toward lay life depicted in the story which apparently comes from St. Bernard of Clairvaux had something to do with it.
The world was like a huge sea which had to be crossed to attain salvation. Monks crossed over a bridge and so didn't even get wet. Diocesan clergy made use of St. Peter's boat and so they might get wet and encounter dangers. Married people had to swim across and encountered many dangers in the process including drowning.
So pious laity tried hard to be like monks, sometimes even directing that they be buried in a monk's habit. Maybe they hoped to fool St. Peter when they got to the pearly gates!
Seriously, third orders arose from the desire of many people to live a fuller Christian life. So, they formed associations of the laity whose members continue to live their ordinary style of life while striving to follow Christ more closely with the help of a papally-approved rule under the direction and in the spirit of a religious order.
Similar to religious orders in their purpose, their rule and papal approval, they differ in that they retain their property, don't make public vows nor do they usually live in community. They are called "third" simply because religious orders of men and women who make public vows are called first and second orders respectively.
St. Francis of Assisi organized the first third order and its rule was approved by the pope in 1221. From the 15th century on, other orders were given permission to develop third orders.
Third orders are always affiliated with religious orders. Some, called regular tertiaries, take vows and live in communities while most, called secular tertiaries, continue to live their ordinary life but in the spirit of the order to which they are attached.
Basically, third orders are groups of lay men and women who have the spiritual support from a religious order while they try to live out a strong religious commitment.
Today, we have a variety of lay groups and a number of them exist within our own archdiocese. Third orders still continue.
In addition, within recent years, religious congregations of men and women have established "associates" who share their spirit and often their apostolate. Lay women and men as well as clergy can become associates.
The Catechism refers to secular institutes as institutes of consecrated life whose members commit themselves to the evangelized counsels of poverty, chastity and obedience, usually for one or more years at a time but usually live in the "world." It also speaks of societies of apostolic life without religious vows.
Then, there are a variety of spiritual lay "movements" such as Focolare which are not specifically attached to a religious order. The focus of all of these groups is a more intense Christian life and apostolate for laity living in the "world."
I find it fascinating how all these religious groups, who practise their own form of spirituality, fit into the life of the Catholic Church without having to develop all sorts of splinter groups.
What is a third order?