An adiabatic process (a thermodynamics term) is a physical process that occurs with no transfer of heat. It is the extreme limit for processes that are well-insulated and thus exchange very little heat with their environment. It is basically theoretical (i.e., no insulation is perfect, just as no vacuum on Earth is perfect or no motion on Earth is frictionless), but the concept allows calculation of limits, such as how much it is possible to affect the resulting temperature of a process if you increase its insulation. Modeling an actual process as adiabatic is sometimes a useful approximation.
For example, if a parcel of gas is compressed, its temperature is affected not only by any heat added or removed, but by the compression itself. Thus, in a limiting case of a theoretical perfectly insulated environment (making it an adiabatic process), the temperature would rise purely from the compression. A different limiting case might be to remove just enough heat to exactly maintain the temperature throughout the time to compress the gas, a specific example of a non-adiabatic process.