Congratulations. The degree you are about to receive derives from those marks for which you worked so hard. Your old friend gradire, "to step," contributed not only to your making good grades but, to your degree and to graduating as well. It shows how far you've come, marking your first steps out into the world.
On the other hand, those who are not in attendance have obviously made some serious missteps, which make their absence degrading, (de) literally, a "step marked down."
The sheepskin you hold in your hand dates from the 15th century, a time when the skin of the sheep was used for parchment. This document symbolizes how we separate the sheep from the goats, distinguishing between the worthy and the unworthy. Its validation can be found in Jesus' prophesy of the Last Judgment in Matthew 25:31 that the sheep (the innocent) will sit on God's right hand (and find salvation) and the goats (the corrupt) will sit on the left (and be sent to damnation).
A diploma (dis + plus) was once literally "a document twice folded." In reality it's more often now a single sheet, something simpler, from the Latin, simplus, "without a fold." What isn't simple, however, is that you are now counted among the "chosen" and placed within the fold.
What you hear in the background are the strains of Elgar's Pomp and Circumstance. The pomp is courtesy of the Greek pompe, "religious procession" and the circumstance comes from the Latin circum, "around," and stare, "to stand, "leaving your parents proudly assembled — standing proof that you are now a better person, though such evidence is at best circumstantial.
Bright-eyed, bushy-tailed, you now join the flock. The world awaits you. A bright future lies ahead. It's your rendezvous with destiny! ... Long and sustained applause.