A Blizzard Warning is a National Weather Service alert for sustained wind or frequent gusts of 35 mph (56 km/h) or more with falling or blowing snow that frequently cuts visibility below a quarter mile (0.4 km) for three consecutive hours or more. It is driven by wind and visibility, not by how much snow falls.
Three conditions at once
All three parts have to come together: wind at or above 35 mph, sustained or in frequent gusts, visibility frequently below a quarter mile in snow, and a duration of at least three hours in a row.
NWS Instruction 10-513 spells these numbers out directly, while it leaves the snow and ice amounts for other winter warnings to be locally defined. The Twin Cities and Des Moines offices, for example, list the same blizzard criteria.
Snow already on the ground counts
The criteria say falling and/or blowing snow. Wind lifting an existing snowpack and cutting visibility with no new snow falling is called a ground blizzard, and it can meet the same thresholds.
Older definitions of a blizzard also required low temperatures, but the current NWS criteria do not. Dangerous cold is handled by separate products.
Where it sits among winter alerts
There is no separate Blizzard Watch anymore. It was folded into the Winter Storm Watch on 10/01/17, and a watch for blizzard conditions alone carries the line "Blizzard conditions possible."
Snow Squall Warnings are not issued while a Blizzard Warning or Winter Storm Warning is in effect.
Reading the warning
The word "frequently" matters. Visibility does not have to stay below a quarter mile the whole time, so conditions inside a warning can change quickly from place to place and moment to moment.
Wind chill is no longer part of the winter storm product suite. Wind chill alerts were moved into the Extreme Cold products, which now carry names such as Extreme Cold Warning and Cold Weather Advisory.