Straight up it refers to a "snack" between meals, but as slang the snack is preferably a crotch, be it male or female, depending upon your preference.
According to the Oxford
Dictionary it is of Yiddish origin. The other Yiddishism commonly linked to going down is to fress.
The Brits do get credit for expanding on it with a "nosh-up", a large meal. So you can bloody well stuff it up your arse John Bull.