Displacement from the area under a velocity–time graph

At constant velocity, displacement $= v \times t$: the area of a rectangle of height $v$ and width $t$.

When $v$ changes, slice the time into thin strips of width $\Delta t$. In each strip the velocity barely changes, so the strip's area $v \times \Delta t$ is the small displacement $\Delta s$ in that time. Add up all the strips and you get the whole area, and the whole displacement.

Units agree too: $\text{m s}^{-1} \times \text{s} = \text{m}$.