Let's imagine how a given category is a monad in a bicategory of spans.
Consider the set of all the objects in the category C0 and the set of all the morphisms in the category C1 (they're all muddled together in this set). We have two functions domain : C1 -> C0 and codomain : C1 -> C0 which assign to each morphism its source and target object.
This pair of functions forms a "span" of sets, which is a diagram of this shape:
C_1
╱ ╲
dom cod
╱ ╲