A/C to 1st law of thermodynamics;
dQ= dU + PdV
For adiabatic process, dQ=0
So, dU + PdV=0
or, dU = -PdV
When the expansion takes place, volume of the gas increases i.e. dV = +ve, hence dU = -ve
i.e. internal energy of the gas decreases and hence the temperature falls.
If the gas is compressed, volume of the gas decreases, i.e. dV = -ve, hence dU = +ve; i.e.
internal energy of the gas increase and hencew its temperature increase.
Hope this clarifies your doubt.