Answer
A process during which a system remains close to an equilibrium state at all times.
It helps the engineering studies to be easier to solve.
Work Step by Step
A quasi-equilibrium process is when the process proceeeds in such a manner that the system remains infinitesimally close to an equilibrium state at all times.
It is important in engineering because many processes can be approximate to a quasi-equilibrium process and these make them easier to solve and also in a process in quasi-equilibrium the work output of a device is maximum.