A blizzard is a large winter storm, characterized by heavy snowfall and accompanied by high winds. We're not talking flurry or a snowsquall. It's the kind of snow storm you read about.
If you had to shovel 5 inches of snow off of your sidewalk, the snow storm was probably just a snow storm, an annoyance perhaps but not a blizzard. A blizzard is a huge snowstorm that results in the disruption of normal activities. Offices close, schools are shut down, streets are snow-packed, and people stay at home. The word can also be used figuratively, to mean "a rash" of something — like the blizzard of insurance forms you had to complete after surgery.