This theory is an attempt to explain how some people escape the discomfort of cognitive dissonance. A behaviour is justified internally so as to place themselves in accordance with their action.
In an exemplifying study by Festinger and Carlsmith participants performed a boring task and were instructed to tell the next participant that they had enjoyed it. One group was paid $1 to lie while another was paid $20. Those who were paid less actually reported a higher level of enjoyment of the task; an internal justification. The $20 group already had an external justification for their behaviour (the money).