The definition of an Hour Angle is: the arc of the Equator or Equinoctial intercepted between the meridian of a datum and the meridian of a celestial body, measured westward from 0º to360º.
That may be the dictionary definition but, in more simple terms, just as declination is like latitude, but projected out into space, so Hour Angle is analgous to Longitude (or change of longitude) projected out into space.
Hour angle is always measured clockwise (looking down from the North Pole) or westwards, even if it's more than 180º. It can either be measured from Greenwich, in which case it's called the Greenwich Hour Angle (or GHA), or it can be measured from from any nominated datum longitude. The most usual case other than GHA is from the longitude of the aircraft or ship taking the astronomical observation, in which case it is called the Local Hour Angle (or LHA).