A major hurricane is a hurricane that reaches Category 3 or greater on the Saffir-Simpson scale. This means that its one-minute sustained winds are 111 mph or greater. This includes Categories 3, 4 and 5. With hurricanes, a very small increase in wind speed can translate to a very large difference in the amount of damage that it causes. A storm at 100 mph (Category 2) might leave a home with only cosmetic damage, while at 120 mph (Category 3), it might totally destroy it. So there is some sense in having a granular scale, with a clear dividing line between "normal" hurricanes and "major" hurricanes, but where the line is drawn is somewhat arbitrary.
It also can be somewhat misleading, since there are other things that determine whether a hurricane is dangerous than merely its wind speed. The size of the storm, and its precipitation, as well as the terrain it travels over, are as important as the raw wind speed. At times, such as with Hurricane Sandy in 2011, or the recent Hurricane Florence, a nominal change in the designation of the storm led people to underestimate how damaging it would be.
The designation of "major hurricane" is a useful definition, but like all designations or categories, it is only a tool for understanding complex natural phenomena.