Let us take a container having some gas and to compress there is a piston to move up and down and the gas exerts some pressure on the piston. At that position, the temperature and the pressure of the gas becomes same as the surroundings of the container, so there is thermal equilbrium between the gas and surroundings. When the piston is moved down with external pressure, then the pressure of the gas is different from the pressure of surroundings and the temperature of the gas is different from the temperature of the surroundings because the gas undergoes sudden compression due to moving down the piston.
We stop the piston moved down, after some time again gas reaches the equilbrium with the surroundings of the container, i.e., gas takes some time to reach equilbrium.
In our hypothesis, if we take ideal gas and the piston is moved down infinitesimally slow, then each and every stage gas reaches the equilbrium with surroundings of the container. Like this, at every stage the temperature and the pressure are same as the surroundings. In general, it is not happened and it is difficult to moved down the piston with infinitesimally slow manner.
So, this hypothetical process is called quasi-static process.
Basing on this process, we can step up to know about isothermal, adiabatic processes.
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