In case of positive displacement type compression, the phenomenon of decreasing volume of air, causes increase in pressure. In case of centrifugal type compression, during each increase in velocity the kinetic energy of the air is increased, and during each decrease in velocity this kinetic energy is converted into an increase in pressure.
Animation showing relationship between pressure and volume when mass and temperature are held constant.
(See also, ‘Compressed air’, ‘Air Compressor types’)