Regalia in the past...
As described in the article on the GraduationSource website, graduation attire came to fruition when universities began developing in the 12th and 13th centuries. Historians connected the attire of long robes to the scholars staying warm in the unheated buildings during this time, in addition to wearing them in order to distinguish themselves from the townspeople.
This drawing depicts what may have been worn during this time, seen in the image is scholars and professors wearing robes and caps.
While medieval schools were the inspiration behind academic dress, Oxford and Cambridge were the first to officially recognize graduation attire. By later years, excessive wear was banned and it was important that everyone had cohesive outfits in order to create unity during the ceremony.
Shown in this image is Andrea Mantegna (left) and Linus Pauling (right) although these images were about 500 years apart there is a distinct feature, being the graduation headwear, an important part of the regalia. Although there have been variations of the graduation hat in the past, the most common style is the mortarboard cap. Historians believe that the square shape of the cap originates from the form of a book to represent the scholarly wear, or even the shape of the Oxford quad. As I mentioned earlier this was one of the first schools that formally recognized graduation wear. Even with the uncertainty of the origin, it remains popular amongst education institutions.