Bill Phillips identified a negative correlation between rates of unemployment and inflation across a range of countries, which became known as the Phillips curve. The reason for this is that when inflation is high the economy is usually operating at or close to full capacity, so lower unemployment.
When more people are seeking work this usually means that there is an economic downturn and therefore less inflationary pressure. This became known as the Short Run Phillips Curve
The Long Run Phillips curve is vertical at the non-accelerating inflation rate of unemployment (NAIRU). Any attempt to boost AD and reduce unemployment in the short run, will lead to higher inflation expectations.
Wage demands rise and the demand for labour falls, pushing unemployment back to its natural level (NAIRU). There is a direct parallel between the vertical LRPC and the vertical LRAS curve.
The policy implications of the SRPC are to suggest governments can either accept higher inflation in exchange for bringing down unemployment OR keep inflation low and stable and accept higher unemployment. However this trade off does not exist in the long run, where attempts to reduce unemployment trigger accelerating inflation, and fail to sustain lower unemployment anyway. The argument would therefore be to focus on supply side improvements to the economy rather than trying to tinker with unemployment or inflation using demand side policies.
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