Stagflation typically comes from a negative supply shock: energy, food or a disruption to production capacity. Output falls and prices rise together, which is the opposite of a demand shock where both move the same way.
For markets it is the worst regime, because bonds and equities fall together. The usual defensive correlation breaks down, since the bond leg is being hurt by inflation at the same time the equity leg is being hurt by growth. tips, commodities and cash tend to be the only shelters.
Example: gdp growth prints minus 0.4% annualised while core inflation runs 5.2% and unemployment rises 0.5 points. A taylor-rule using the inflation gap demands hikes; the employment leg of the dual-mandate demands cuts.
Related: disinflation, phillips-curve, dual-mandate, recession, tips