The hour angle is an expression describing the difference between local solar time and solar noon. Although it is calculated directly from measurements of time, it is expressed in angular units, typically degrees.
The hour angle measures time before solar noon in terms of one degree for every four minutes, or fifteen per hour. Time after solar noon is expressed using a negative hour angle. Therefore, at two hours before solar noon the hour angle is 30 degrees, and at two hours after solar noon it is -30 degrees. This chart depicts the relationship between the hour angle and local solar time ("N" represents North but would be South in the Southern Hemisphere).
Note that the hour angle does not represent the altitude of the sun in the sky because it is a meaurement of time. The sun rises and sets when its altitude is zero degrees, not necessarily when its hour angle is +/- 90 degrees.