The Javalambre Photometric Local Universe Survey (J-PLUS ) is an ongoing 12-band photometric optical survey, observing thousands of square degrees of the Northern Hemisphere from the dedicated JAST/T80 telescope at the Observatorio Astrofísico de Javalambre (OAJ). The T80Cam is a camera with a field of view of 2 deg2 mounted on a telescope with a diameter of 83 cm, and is equipped with a unique system of filters spanning the entire optical range (3500-10 000 Å). This filter system is a combination of broad-, medium-, and narrow-band filters, optimally designed to extract the rest-frame spectral features (the 3700-4000 Å Balmer break region, Hδ, Ca H+K, the G band, and the Mg b and Ca triplets) that are key to characterizing stellar types and delivering a low-resolution photospectrum for each pixel of the observed sky. With a typical depth of AB ¿21.25 mag per band, this filter set thus allows for an unbiased and accurate characterization of the stellar population in our Galaxy, it provides an unprecedented 2D photospectral information for all resolved galaxies in the local Universe, as well as accurate photo-z estimates (at the δ z/(1 + z)¿0.005-0.03 precision level) for moderately bright (up to r ¿ 20 mag) extragalactic sources. While some narrow-band filters are designed for the study of particular emission features ([O II]/λ3727, Hα/λ6563) up to z < 0.017, they also provide well-defined windows for the analysis of other emission lines at higher redshifts. As a result, J-PLUS has the potential to contribute to a wide range of fields in Astrophysics, both in the nearby Universe (Milky Way structure, globular clusters, 2D IFU-like studies, stellar populations of nearby and moderate-redshift galaxies, clusters of galaxies) and at high redshifts (emission-line galaxies at z ≈ 0.77, 2.2, and 4.4, quasi-stellar objects, etc.). With this paper, we release the first ¿1000 deg2 of J-PLUS data, containing about 4.3 million stars and 3.0 million galaxies at r < 21 mag. With a goal of 8500 deg2 for the total J-PLUS footprint, these numbers are expected to rise to about 35 million stars and 24 million galaxies by the end of the survey.