What is Extraordinary Form?
"Novus Ordo" is the technical term for the form of Mass that we are all familiar with today. It has been the norm since 1970, after Mass went through a reform following the Vatican II council. It is typically celebrated in the vernacular language with the priest facing the people, and there is more freedom to make small adjustments within the liturgy, and it does a good job of engaging the people in prayer.
What is now the extraordinary form is the traditional form of the Mass entirely in Latin, which was the norm until the 1960s. It hadn't been in wide use since the 1970s, but in 2007, Pope Benedict XVI expanded its use to the entire universal church, saying that it was never abrogated and affirmed that it is an extraordinary form of today's Mass. While the "novus ordo" remains the ordinary form, he opened the doors to the use of this Mass so that its theological richness, steeped in tradition of the Church, may influence our worship of God moving forward. It takes a little getting used to if you've never attended, but once you begin to appreciate it, it can be tremendously helpful in drawing you into prayer and focusing on the sacrifice being offered to God, and understanding what Mass is truly about.
Click here to read Pope Benedict XVI's Motu propio Summorum Pontificum on the use of the Roman liturgy prior to the reform of 1970