From 1 April 2019 to 27 March 2020, the Advanced Virgo detector, together with the two Advanced LIGO detectors, conducted the third joint scientific observation run O3, aiming for further detections of gravitational wave signals from astrophysical sources. One of the upgrades to the Virgo detector for O3 was the implementation of the squeezed light technology to improve the detector sensitivity beyond its classical quantum shot noise limit. In this paper, we present a detailed description of the optical setup and performance of the employed squeezed light source. The squeezer was constructed as an independent, stand-alone sub-system operated in air. The generated squeezed states are tailored to exhibit high purity at intermediate squeezing levels in order to significantly reduce the interferometer shot noise level while keeping the correlated enhancement of quantum radiation pressure noise just below the actual remaining technical noise in the Advanced Virgo detector.