The mass that we celebrate as the "Extraordinary Form" today, was celebrated according to ancient custom in Latin from the time of the Council of Trent in in 1564 until the Vatican II Council in 1962 when the last Latin missal was published before the Novus Ordo, also known as "the Mass of Pope Paul VI" was first promulgated in 1965. Thus, for approximately 400 years, the Tridentine Mass was the mass celebrated by most Catholics.

This mass has many differences but also many similarities to the Novus Ordo.  The primary difference is that the priest faces away from the assembly.  This is because he is leading the congregation in prayer.  He also speaks very quietly and, often times, cannot be heard by the faithful.  

As Pope Emeritus Benedict XVI said at the promulgation of his motu proprio, our current missal and the Extraordinary Form are two celebrations of the same rite that, although appealing to only a very small percentage of Catholics, needs to be offered if there are a significant number who request it.

In 2007, the Vatican published a document called Universae Ecclesiae in which they explained that the purpose of the return of the 1962 Missal was to:

1. offer to all the faithful the Roman Liturgy in the Usus Antiquior (the "More Ancient Use"), considered as a precious treasure to be preserved;
2. effectively guarantee and ensure the use of the Extraordinary Form of the Mass for all who ask for it, given that the use of the 1962 Roman Liturgy is a faculty generously granted for the good of the faithful and therefore is to be interpreted in a sense favorable to the faithful who are its principal addressees;
3. and, promote reconciliation at the heart of the Church.