The relationship between senior students and junior students is one with its origins not in martial arts, but rather in Japanese and Asian culture generally. It underlies Japanese interpersonal relationships in many contexts, such as business, school, and sports. It has become part of the teaching process in Japanese martial arts schools. A senior student is senior to all students who either began training after him or her, or who they outrank. The role of the senior student is crucial to the indoctrination of the junior students to etiquette, work ethic, and other virtues important to the school. The junior student is expected to treat their seniors with respect, and plays an important role in giving the senior students the opportunity to learn leadership skills. Senior students may or may not teach formal classes, but in every respect their role is as a teacher to the junior students, by example and by providing encouragement. – From Wikipedia
Basically, the senior student is second in command to the instructor. He/she the senior student for a reason. He/she has dedicated themself to learning the art and seeing it progress. He/she has seen the school change and many students pass through the doors. The senior student is a role model and great resource on how things are to be done in the class. In the absence of the instructor, the senior student may run the class.
– Sensei Chris Love