A commencement is the act of starting out, or blazing a new trail.
The suffix -ment makes the word commencement a noun — a thing, an activity, a start. The word can be used for the beginning of anything, from a business meeting to a vacation trip to a marriage. Anything that begins has a moment of commencement. That's why a graduation ceremony is called a commencement — a graduate is embarking on a new life, and the commencement ritual marks the official beginning of that life.