Quasi-experiments are studies which lack the control of a true experiment because one or more of its requirements cannot be met, ex: deliberate use of an independent variable or random assignment of subjects to different groups.
Studies of the effects of drugs on pregnant women are based on data about women who have already been pregnant and either taken or not taken drugs. Researcher can’t control assignment of subjects or choices presented to them, but can measure differences between the two populations and obtain significant findings. Such studies provide a basis for investigations that would otherwise be impossible.
Source: Gale Encyclopedia of Psychology
A quasi-experiment is one that applies an experimental interpretation to results that do not meet all the requirements of a true experiment. It means when the situation is such that the experimenter has some control over the manipulation of independent variables but fails to arrange for the other basic requirement of a true experiment, which is, creating equivalent groups.