It is sort of an empty phrase that was used as part of an anti-drug campaign.
It meant that if parents got closer to their children, to the point of hugging them more, then their children would not feel as alienated and therefore would not be as likely to use drugs.
It was about as effective as the slogan "Just say no." - When friends offer you drugs or a boy pressures a girl to have sex, they should just say no. It would be good if that happened, but empty slogans won't be the motivating factor.