Hg, in terms of vacuum, is an abbreviation for either millimeters or inches of mercury, depending on the type of measurement. Mercury is a metal on the periodic table of elements with a symbol of Hg.
Vacuum gauges are used to diagnose engine problems by measuring manifold pressure. A measurement of 0 Hg is equal to atmospheric pressure, and anything below atmospheric pressure is referred to as a vacuum. The measurements (in either inches or millimeters of mercury) show a vacuum's ability to support mercury in a tube to a height of whatever is measured. Thirty inches of mercury is considered an effectively perfect vacuum, although it is impossible to achieve a truly perfect vacuum. Higher vacuum gauge measurements typically indicate a healthier engine.