A Constant is a value that remains the same. When conducting an experiment, it is important for the researcher to maintain control over the many variables that could affect what he is trying to investigate. Ideally, when a researcher designs an experiment, the only thing that should vary is the thing under study. All other factors that could affect the outcome must be strictly controlled by keeping them Constant.
For example, a researcher is interested in finding out if breastfeeding led to higher IQ in children. Many factors could affect IQ, like socioeconomic status, mother's age, or family setup, among other things. In order to make sure that any differences in IQ can only be attributed to the type of feeding received as a baby, the experimenter must find a way to control all of the other factors that could affect IQ scores. One way of doing that is by turning all of those other factors into Constants.
To do this, the experimenter could select participants that only come from the middle class, with mothers’ age ranging from 25-30 years old, in a nuclear family setup. Ideally, the only thing that would differentiate one group from another would be how they were fed as babies. One group would be children who were exclusively breastfed from birth until weaning, and the other group would be composed of children who were exclusively formula-fed from birth until weaning.