Stagflation is not a state that occurs often because recession reduces demand for goods (because people have less money to spend). Low demand usually leads to low inflation.
The word stagflation is a conflation of stagnation and inflation.
Stagflation occurred in the 70s and 80s. Economic theory prior to that time regarded the combination as unlikely, if not impossible.
Once stagflation occurs it is difficult to deal with. The measures a government would usually take to revive an economy in recession (cutting interest rates or increasing government spending) will also increase inflation.
Under normal recessionary conditions inflationary policies are acceptable, but given already high inflation, pushing inflation still higher is itself damaging.