The speaker in the video below explains the concept of mastery learning by using the example of skateboarding. Mastery-Based Learning is a concept and not a program. This concept is alternatively called competency-based education or proficiency-based learning. At its most basic, the idea is that students will work on achieving mastery of standards and progress through their education as they meet these standards. As students become much more clear about what they are trying to achieve, they can take more ownership over their own learning.
Other relevant resources:
Students at the Center has published this paper on the Today's Competency Education Movement. This paper includes definitions, core elements, and its history.