Definition: the internal texture of a baked good — how open or tight, tender or chewy, the inside is.
“Crumb” is baker’s shorthand for what you see when you break something open. A sponge cake wants a fine, even, tender crumb; a cookie might want a chewy, slightly open one; bread, an airy and irregular one. It’s shaped by everything upstream: how much you creamed, how you mixed, the flour, the fats, the bake. When I say “look for a soft crumb,” I mean the inside should look and feel right, not just the outside.
In practice: the cross-section is the tell — that first slice or snap shows you the crumb.