The area under acceleration-time graph gives
Distance travelled
Change in acceleration
Force acting
Change in velocity
The area under acceleration-time graph gives
Acceleration$-$Time graph represents the object's change in velocity. Acceleration $=\frac{\Delta v}{\Delta t}$
Area between acceleration-time graph gives$:$
$a \times \Delta t=\frac{\Delta v}{\Delta t} \times \Delta t=\Delta v$