A preparation is a different individual course that you are teaching. If you are teaching 2 different sections of the same course in the same semester, that counts as only 1 preparation, but it counts twice towards your teaching load. A teacher's “preparation period” describes the free period that the teacher receives during the day, apparently for “preparation”. But if a teacher asks: “How many preparations do you have? , the query implies the number of separate courses for which the teacher is responsible.
So a teacher could say “I have no preparation, but I'm only teaching one preparation: geometry or “I have three preparations and it's brutal without explaining which preparation is which. For each preparation, the teacher needs to develop a set of lesson plans. Multiple preparations require multiple lesson plans. In many schools, there are a number of preparations for new teachers who may not receive first-choice course assignments.
Other disciplines, such as world languages, may offer several unique courses, such as the German course I. For other departments, there may be specialized courses with only one section, such as AP Physics. Multiple preparations may be the best way to meet student needs. I can have the maximum capacity of students (in my state there are 168 students per high school teacher) but if I only have one preparation, it is easier than four high schools like now.
I wonder if researchers are prone to ignoring high school preparations because they would have to recognize how questionable their conclusions are without considering the preparations. Ultimately, it means more teachers on the payroll or fewer courses offered, because you have to compensate somehow less preparation and less flexibility.
