An adiabatic process is one in which heat is not transferred to or from its surroundings, usually because the process occurs in an insulator or because it happens too fast for heat to transfer from the process to its surroundings.
Another way of saying is this is that an adiabatic process is one in which energy transfer occurs only through work.
An ideal gas that undergoes an adiabatic process can be modeled by the polytropic process equation:
$$ PV^n = constant $$
The work done on the gas increases its internal kinetic energy, which results in a rise in temperature. This is why compressing air increases its temperature.
In contrast to an adiabatic process is an isothermal process.