Ordinary versus Extraordinary Form

I hate to admit this, but I never really understood the difference - I thought it was just an English version versus a Latin version. Thanks to a terrific site called Canons Regular of St. John Cantius, I know understand it better.

 From their site:

Ordinary Form of the Roman Rite. In the Ordinary Form the Mass is celebrated according to the Missale Romanum of 1969, promulgated by Pope Paul VI, which is currently in its third edition (2002). This form is widely celebrated in the vernacular.

 Extraordinary Form of the Roman Rite. In the Extraordinary Form, Mass is celebrated according to the Missale Romanum of 1570. While this Missal was codified at the Council of Trent, it was in use at least since the time of St. Gregory the Great. It is used today according to the 1962 edition, promulgated by Blessed Pope John XXIII during the Second Vatican Council. In accordance with norms of Summorum Pontificum, all Roman Rite clergy may celebrate according to the Extraordinary Form.
 

Why is the Extraordinary Form of the Mass sometimes called the ‘Tridentine’ Mass or the ‘Traditional Latin Mass’?

The Extraordinary Form of the Mass is the patrimony of the Western Church. This liturgy is sometimes called the 'Tridentine' Rite, after the Council of Trent in the sixteenth century. This title is misleading, because the Council of Trent did not invent the liturgy, which was even then already ancient. It is sometimes called the ‘Traditional Latin Mass’ as this Mass is always celebrated in the official language of the Church (i.e. Latin).