Short answers, pulled from the story.
Potential output, also called natural gross domestic product, refers to the highest level of real GDP an economy can sustain over the long run. It is shaped by natural and institutional constraints, including the supply of workers, capital equipment, natural resources, and the reach of technology and management skill.
In a free market economy without wage or price controls, inflation tends to increase when actual GDP rises above potential output. Demand for factors of production outstrips their finite supply, pushing prices up. Graphically, this corresponds to production volume moving above the optimum quantity on the average cost curve.
The output gap, also called the GDP gap, is the difference between potential output and actual output. When the gap is negative, the economy is producing below its sustainable ceiling. The output gap may closely track lags in industrial capacity utilization.
The NAIRU, or natural rate of unemployment, is the unemployment rate expected to prevail when an economy operates at potential output. Economists disagree considerably about what the NAIRU actually is at any given time. Post-Keynesian economists reject the NAIRU concept altogether as non-valid.
When actual GDP falls below natural GDP, suppliers face excess production capacity and cut prices to attract buyers and put idle resources to work. This puts downward pressure on inflation. In some circumstances, prices may decelerate toward outright decline.
Okun's law examines the relationship between percentage changes in real output and changes in the output gap over time. It is one of the analytical tools economists use to study how actual economic performance compares with an economy's potential.