By definition, severe weather comes in three basic varieties: high wind, large hail or a tornado. Any thunderstorm that produces a tornado is obviously considered severe and a Tornado Warning will be issued for any actual tornado or a reasonable likelihood of a tornado based on Doppler radar.
For hail to be considered severe, it needs to be one inch in diameter or larger. A quarter is about an inch wide, so any observed or Doppler-estimated hail one inch or larger is considered severe and will prompt the issuance of a Severe Thunderstorm Warning. Smaller hail will not necessarily result in a warning.
The last parameter for severe weather is wind. When the wind produced by a thunderstorm reaches or exceeds 50 knots (58 mph), it is considered severe. It is possible for a storm to contain two or even all three of these severe conditions at the same time.