The masters seminar is the capstone experience of the Master (or BA/MA) program. Each masters student chooses a field of mathematics in which they want to deepen their understanding, and does an independent study in that topic, coupled with weekly presentations.
Some topic choices are very close to traditional course material (Algebraic topology, Logic, etc), and some are more uniquely specialized (Elliptic Curves, Growth of algebras, etc). The topic is chosen by the student in collaboration with a faculty mentor.
Each seminar student gives a weekly presentation to a small (3-4 member) faculty audience, and receives informal feedback about both the mathematics and the talk. Of course this is intimidating at first but students quickly understand that faculty are acting as coaches, not judges. At the end of the seminar each Masters student prepares a one-hour talk to the department. Many students find it exciting to reverse the usual teacher/learner roles and explain to the faculty. The success of this talk is usually the last requirement for graduation with a Masters degree in Mathematics.