This is the idea that humans fill in gaps in vague statements to make them sound personal to them. Barnum is in reference to PT Barnum who ran sideshows in the late 19th century. Barnum hosted several hoaxes as part of his show and was said to be a very persuasive speaker.
This is most evident when engaging with people who have been to a psychic or a medium. If you ask them after their event they will tell you that the psychic knew lots of really specific detail about them. When in reality they have heard cold reading statements as very specific statements about them.