The story
By analogy with cutting a sandwich having three layers (two of bread and one of ham), for the case where n=3.
Etymology from Wiktionary, CC BY-SA 4.0.
ham sandwich theorem
Today it means: A theorem stating that, given n measurable "objects" in n-dimensional Euclidean space, it is possible to divide all of them in half (with respect to their measure, i.e. volume) with a single (n−1)-dimensional hyperplane. Full definition →