Basically Hypnopaedia is "sleep teaching". It is meant to condition the brain towards promiscuity, use of soma, and complete acceptance of society. Through subliminal messages, people are conditioned for the excesses of society via hypnopaedic slogans such as "a gramme is better than a damn". The use of hypnopaedia strengthens the conditioning and indicates the subversive nature of the state. Huxley is showing the readers that propaganda starts at birth and can occur even when we are unaware of it, as when sleeping. He reinforces the point that people are unaware of how influential the propaganda is by constantly having his characters quote "hypnopaedic phrases."
The goal of the state is to ensure social stability, and the conditioning creates the "community" by segregating each infant into separate classes. This promotes stability by creating a group of workers with state-controlled preferences. Thus, economic stability comes from creating preferences that promote spending.