The brain is an argument. We make different decisions in different ways. In addition, different parts of the brain respond to stimuli in different time frames. Think of two teams of lawyers doing discovery to prepare for a trial, and you've got the picture. The fMRI scans support the notion put forward by Jonah Lehrer that the brain is an argument. How we settle that argument depends on social context, prior experience, etc.
They mean that within the brain different processes/parts of the brain interpret things in different ways and then compete (ie argue) with each other to provide the "final" interpretation or perception.