From an article of the same title by Daniel Goleman in the NY Times:

The hallmark of the flame is...thoughts expressed while sitting alone at the keyboard [that] would be put more diplomatically — or go unmentioned — face to face.

Flaming has a technical name, the "online disinhibition effect," which psychologists apply to the many ways people behave with less restraint in cyberspace.

The emerging field of social neuroscience, the study of what goes on in the brains and bodies of two interacting people, offers clues into the neural mechanics behind flaming.

This work points to a design flaw inherent in the interface between the brain's social circuitry and the online world. In face-to-face interaction, the brain reads a continual cascade of emotional signs and social cues, instantaneously using them to guide our next move so that the encounter goes well. Much of this social guidance occurs in circuitry centered on the orbitofrontal cortex, a center for empathy. This cortex uses that social scan to help make sure that what we do next will keep the interaction on track.

Research by Jennifer Beer, a psychologist at the University of California, Davis, finds that this face-to-face guidance system inhibits impulses for actions that would upset the other person or otherwise throw the interaction off.