is a $\kappa$-accessible functor (for $\kappa$ a regular cardinal) if $C$ and $D$ are both $\kappa$-accessible categories and $F$ preserves $\kappa$-filtered colimits. $F$ is an accessible functor if it is $\kappa$-accessible for some regular cardinal $\kappa$.

The theory of accessible 1-categories is described in

Michael Makkai, Robert Paré, Accessible categories: The foundations of categorical model theory Contemporary Mathematics 104. American Mathematical Society, Rhode Island, 1989.1989.