Why belts are so important?

Belts have absolutely no meaning outside the dojo. Within the classroom, they do have value. Basically, the belt helps the instructor and other students set their expectations. This can even help promote safety. For example, if two students are paired to spar, the senior student assumes the roles of assisting the instructor. Instead of just going full force and annihilating the less experienced student, he should take the opportunity to teach, slow down a little and explain what to do.