The “Mysore” style of teaching is the traditional way this methodology was taught by Sri K Pattabhi Jois in Mysore, India and continues now with his Grandson, Sharath Jois.
The Mysore style of yoga asana practice is a particular way of teaching yoga within the Ashtanga Yoga tradition as taught by Sri K. Pattabhi Jois and Sharath Jois in the southern Indian city of Mysore. There are some differences in this method from the usual modern way in which yoga is taught:
The class is not "led" as a whole but rather all instruction is one-on-one within the group class setting
Students practice their own portion of the Ashtanga sequence of asanas at their own pace as given by teacher
The teacher assists each student individually by giving physical adjustments & verbal instruction
In Mysore style students learn the fixed order of asanas using a specific movement-breathing technique called vinyasa. Through vinyasa, there is continuity via the breath from asana to asana. In the Ashtanga sequence, each asana builds from the previous – and prepares for successive – asanas.
Each student is given their yoga routine according to their ability. Newer and beginner students tend to have a much shorter practice than do those with more experience. As one gains more strength, stamina, flexibility and concentration, additional asanas are given to the student. The sense of the word "given" in this context comes from how the practice is taught in India, where a yoga practice is something that a teacher gives to a student as a spiritual practice. In the West, people are accustomed to learning a lot of asanas all at once – such as in a typical modern "led" yoga class.
Asanas are given, one by one in a sequential order. One by one also means that once a student is given a new asana, they practice their sequence up to that asana, then do backbends if applicable, and then wind down with the finishing sequence. In general, the next asana in the sequence should be added/taught/learned only after obtaining stability in one's last asana.
The Ashtanga vinyasa method – as is any hatha yoga practice – is intended to be a daily practice. Traditionally, practice takes place every day except for Saturdays and full & new moon days which occur about twice monthly.
Here are some fun links to get an idea of what a Mysore Practice is like: