The best way to explain the tradition would be to understand what people give up to march. Whether you march 1, 3, 5, or- dare I say- 7 years in DCI, you give up a lot of things you could otherwise being doing. You give up your summers, your weekends, a LOT of $$$, and in many instances, the health of your knees. After experiencing something that touches you as much as living and performing with your adopted family for months on end, the activity shapes who you are and what you will become in the future. Leaving something on the field after your last performance ever is a way to say that you're leaving a little part of yourself on that field, and no matter how much you wish you could continue having those experiences, you are done. Forever.
Its a way to recognize that a very significant chapter in your life has come to an end, and I'm sure that anyone who has aged out will back me up on that.