Effect size is the magnitude of a treatment effect. It is commonly measured as the difference between the Means of the treatment and control groups, divided by the pooled standard deviation. It may also be expressed as a correlation between the two variables under study, or as an odds-ratio, in the case of binary data.
Sometimes, a treatment effect may be statistically significant but may not be of practical value to the study. In this case, it helps to know the effect size, so that the researchers can make an informed decision about the treatment. In fact, good research studies are designed by starting with the effect size that it is desired to detect, which determines the optimum sample size required to detect that effect size with a certain power.
Effect size is an important consideration in power and sample size calculations for significance tests. It is also used in meta-analysis, where the results of many studies are synthesized to a common metric, effect size, to allow the results to be compared.
Power of a test
This link explains the role of effect size in determining the power of a study. - http://www.poweranalysis.com/effect_size.htm