In oilfield units it is pounds per gallon. Elsewhere it is a specific gravity or kilograms per cubic metre. Hydrostatic pressure at a depth is this density times true vertical depth, not measured depth. In oilfield units, psi is about 0.052 times the mud weight in pounds per gallon times the true vertical depth in feet.
Raising the mud weight is the primary way to stop a kick. Taking the circulating density above the fracture gradient is the usual way to lose returns. The number on the mud report is the static density. The pressure the formation sees while circulating is the equivalent circulating density, which is higher.