A dump that is of such impressive qualities (whether girth, length, odour or texture) that to simply flush it away would be unthinkable. It is therefore carefully transferred from the porcelain bowl to a suitable receptacle (such as a shoebox). At this stage, one can use the shoebox to demonstrate the excellent qualities of saidturd to one's partner / family / co-workers or simply people you pass in the street.
Matt - Has anyone seen Rusty this morning? We're late for a meeting.
Dan - about 20 minutes ago. He was heading towards trap 1 with a newspaper tucked under his arm and an empty shoebox.
Matt - OK. When you see him, make sure to ask him to bring that Shoebox Special with him to the meeting. I think it will really start the meeting off on the right footing.
A discarded shoebox that houses elements that you associate with memorable events in your life. Like your first movie tickets, your best friends' letters to you, birthday cards, pictures of family... etc.
In a sentence: Anna said, "I've never been to a Michael Buble concert before; these tickets are definitely getting parked in my shoebox memories."