A section $𝑠$ of a displayed category over $\mathrm{𝒞︀}$ chooses

1. for each object $𝑐:{\mathrm{𝒞︀}}_0$, a displayed object , and
2. for each morphism $𝑓:𝑐\to 𝑑$, a displayed morphism lying over $𝑓$,

such that $𝑠({\text{𝗂𝖽}}_{𝑐})={\text{𝗂𝖽}}_{𝑠(𝑐)}$ and $𝑠(𝑓\star 𝑔)=𝑠(𝑓)\star 𝑠(𝑔)$.

A section is to a displayed category what a dependent function $(𝑎:𝐴)\to 𝐵(𝑎)$ is to a dependent type: it picks a displayed datum over every base datum.