This means that if a person's statement was recorded and played backwards, the speaker's unconscious thoughts could be heard. The most famous recording that allegedly demonstrates this is the speech given by Neil Armstrong at the time of the moon landing, in which, if played backwards, the words "man will spacewalk" can supposedly be clearly heard.
However it has been argued that without prompting no one would hear this phrase, and only once we had been told what to listen for would we hear it.
The presence of negatively influencing, even satanism-themed reverse speech has been argued to be present in heavy metal music by conservative groups, claiming that this music made or can make their children perform antisocial acts.