Stagflation is the economic nightmare scenario — stagnant growth (or recession) combined with high inflation AND high unemployment, all happening at the same time. It breaks the normal economic rules where inflation and unemployment move in opposite directions.
The most famous example: the 1970s oil crisis. OPEC's oil embargo quadrupled oil prices, causing costs to skyrocket across the economy (inflation) while simultaneously crushing economic activity (stagnation). The US experienced double-digit inflation and unemployment above 9% — a combination economists had thought impossible.
Stagflation is incredibly hard to fix. Raising interest rates fights inflation but worsens unemployment. Cutting rates stimulates growth but fuels inflation further. There is no easy policy solution. Paul Volcker (Fed Chair, 1979-87) eventually broke 1970s stagflation by hiking rates to 20% — triggering a severe recession but finally killing inflation.