To crumble is to come apart into tiny pieces. If the doughnuts you bring to work crumble before you get there, you co-workers will have nothing but crumbs to snack on.
Baked goods seem to crumble easily, but other things tend to crumble too: old houses, over time; sand castles; fragile ruins; and art objects made from clay. Anything that falls apart, especially into small bits, can be said to crumble. The root of the word is the Old English gecrymman, "to break into crumbs," which in turn comes from cruma, "crumb or fragment."