From AMS Glossary
An increase in the central pressure of a pressure system on a constant-height chart, or an analogous increase in height on a constant-pressure chart; the opposite of deepening.
The term is commonly applied to a low rather than to a high. Since filling is almost always accompanied by a decrease in the intensity of cyclonic circulation, it is frequently used to imply the process of cyclolysis. Filling can be defined quantitatively in at least two ways: 1) as the time rate of central-pressure increase; or 2) as that component of the pressure tendency that cannot be attributed to either the motion of the pressure system relative to that point or to the influence of atmospheric tides.