From AMS Glossary
A decrease in the central pressure of a pressure system as depicted on a constant- height chart, or an analogous decrease in height on a constant-pressure chart; the opposite of filling.
The term is usually applied to low pressure rather than to high pressure, although technically it is acceptable in either sense. The deepening of a low is commonly accompanied by the intensification of its cyclonic circulation, and the term is frequently used to imply the process of cyclogenesis. Deepening can be quantitatively expressed in at least two ways: either 1) as the time rate of central-pressure decreases; or 2) as that component of the pressure tendency at any fixed point that is attributable neither to the motion of the pressure system relative to that point nor to the diurnal influence of atmospheric tides.