Gaia Data Release 3 contains a wealth of new data products for the community. Astrophysical parameters are a major component of this release, and were produced by the Astrophysical parameters inference system (Apsis) within the Gaia Data Processing and Analysis Consortium (DPAC). The aim of this paper is to describe the overall content of the astrophysical parameters in Gaia DR3 and how they were produced. In Apsis, we use the mean BP/RP and mean RVS spectra along with astrometry and photometry, and we derive the following parameters: source classification and probabilities for 1.6 billion objects; interstellar medium characterisation and distances for up to 470 million sources, including a 2D total Galactic extinction map; 6 million redshifts of quasar candidates; 1.4 million redshifts of galaxy candidates; and an analysis of 50 million outlier sources through an unsupervised classification. The astrophysical parameters also include many stellar spectroscopic and evolutionary parameters for up to 470 million sources. These comprise T_eff, log g, and [M/H] (470 million using BP/RP, 6 million using RVS), radius (470 million), mass (140 million), age (120 million), chemical abundances (up to 5 million), diffuse interstellar band analysis (0.5 million), activity indices (2 million), Hα equivalent widths (200 million), and further classification of spectral types (220 million) and emission-line stars (50 000). This paper is the first in a series of three papers, and focusses on describing the global content of the parameters in Gaia DR3. The accompanying Papers II and III focus on the validation and use of the stellar and non-stellar products, respectively. This catalogue is the most extensive homogeneous database of astrophysical parameters to date, and is based uniquely on Gaia data. It will only be superseded by Gaia Data Release 4, and will therefore remain a key reference over the next four years, providing astrophysical parameters independent of other ground- and space-based data.