The wizard's diploma is the proof of bearing the title of Wizard. It is given to anyone who graduates from the School of Magic.
After Twinsen completes the three tests for becoming a wizard, the rector gives him the diploma and tells him to sarch for Chedil Amiradoo for the wizard's parade tunic. Twinsen inmediatly gains the second level of magic. When he shows the diploma to Chedil Amiradoo, he recieves the parade tunic, and he can buy orange powder from then on.
In the twinsonian souvenir shop in Zeelich, Twinsen can sell his diploma for 20 zlitos. He can buy it again for 40 zlitos or wait until later in the game, when the attendant of the shop is replaced with an informant, then he can kill him and take the diploma for free.
"Your diploma in magic has allowed you to reach the green ball level of magic."