The drug in question here is soma, a hallucinogen used by those in power to subdue the citizens in Brave New World's futuristic, totalitarian setting. It is described as "the perfect drug," with all the benefits (calming, surrealistic, ten-hour long highs) with none of the drawbacks (no guilt, no hangovers). The citizens of the "World State" have been conditioned to love the drug, and they use it to escape any momentary bouts of dissatisfaction. The problem, as one character identifies, is that the citizens are essentially enslaved by the drug and turned into mindless drones. No drawbacks indeed.
The need for soma represents the failure of the World State to adequately satisfy its citizens.
Soma is the World State's most powerful tool to subdue and control its citizens. Without soma, even hypnopaedia would be ineffective.