My first thoughts were of the ceremonial aspects of the word. But, alas, I have no interesting memories of this traditional rite of passage. I loathed high school and graduated college between semesters so no ceremony.
Having exhausted that aspect I decided to go to the dictionary where to my surprise I found the #1 definition to be: graduation - a mark on an instrument or vessel indicating degrees or quantity.
This brought to mind my quite old and very worn glass measuring cup whose graduation marks have disappeared. I did purchase a replacement, nicely marked and more functional, but still keep the old one. It remains useful.