Graduation itself is a ritual that began in the 13th or 14th century when colleges and universities first began to make an appearance in England. Traditionally, both caps and gowns were black up until the end of World War II, when colorful ensembles began making an appearance.
Tassels are fastened to the center of the mortarboard and hang to the right side of the cap. However, if you are receiving a master's degree or doctorate, your tassel will hang on the left and move to the right. Tassel color when graduating typically represents the type of undergraduate degree you are receiving.
You are often signaled to flip your tassel right after receiving your degree or after walking off stage. Mostly, it depends on your school's traditions. No one knows exactly where this tradition first started, but it is believed to have begun as recently as 40 to 50 years ago, as of 2011.