The natural rate of unemployment is the level of unemployment an economy tends towards when it is neither overheating nor slumping, made up mostly of frictional and structural joblessness. Milton Friedman and Edmund Phelps developed the idea in the late 1960s. Its modern form is the NAIRU, explained in full on that page.
The idea challenged the stable trade-off of the original Phillips curve: pushing unemployment below the natural rate was expected to raise inflation rather than buy lasting jobs.