The paragraph below is from the Wiley Online Library. I would add that enrichment is done to obtain a faster identification of whether or not the new drug works in the selected population and can be very important when that population is comparatively rare, as in subgroups of oncology.
Enrichment designs usually consist of two or three stages, where the first stage serves as a screening process for selecting a certain subpopulation, and the succeeding stages serve to distinguish the treatment effect from the placebo effect, within the selected (enriched) subpopulation. The efficiency of its efficacy (response) detection comes at the expense of the ability to make inferences for the general population; that is, the results are valid only for the selected subpopulation. At the same time, if a valid partitioning of the population is proven, then it might be viewed as evidence of “latent” classifiers, which can be targeted for a search. Statistical analysis commonly makes explicit use of the outcomes from only the selected subpopulation (final stage). Some simple models can take advantage of the outcomes from all stages. Most published studies using these designs have been conducted in the field of clinical oncology, but enrichment designs have become increasingly popular in various therapeutic areas.