The 2-category $\mathsf{Rel}$ is a category with sets as $0$-cells, relations as $1$-cells (with relation composition as composition), and inclusions as $2$-cells (with vertical composition being the fact that inclusion is a preorder, and horizontal composition being the fact that relation composition respects inclusions.)
What is a monad in this category?
A monad in $REL$ is a preorder on a set. To see this, note that we need a $1$-cell $R: A \to A$, a relation, such that we have $2$-cells:
$$\eta: id_A \to R$$ $$\mu: R \circ R \to R$$
but these are just inclusions $id_A \subseteq R$ and $R \circ R \subseteq R$.
$id_A \subseteq R$ means that if $x=y$ then $x R y$.
$R \circ R \subseteq R$ means that if $\exists y. xRy \wedge yRz$ then $xRz$.
These two conditions are the axioms of a preorder.