To "master the concept" means to fully understand and be able to successfully apply a specific idea or theory. It implies gaining deep knowledge and expertise in that particular concept. Full definition
And because he would not want to pee on his hero he will quickly master the concept of the potty to keep clean. (toptenstrollers.com)
During and after reading, it enhances discussion of texts and helps students master concepts that seem simple but become more complex under examination. (tolerance.org)
I always tell my students they have not mastered a concept until they can teach it successfully to their peers. (blog.classtag.com)