The Javalambre-Physics of the Accelerating Universe Astrophysical Survey (J-PAS) will scan thousands of square degrees of the northern sky with a unique set of 56 filters using the dedicated 2.55 m Javalambre Survey Telescope (JST) at the Javalambre Astrophysical Observatory. Prior to the installation of the main camera (4.2 deg² field-of-view with 1.2 Gpixels), the JST was equipped with the JPAS-Pathfinder, a one CCD camera with a 0.3 deg² field-of-view and plate scale of 0.23 arcsec pixel⁻¹. To demonstrate the scientific potential of J-PAS, the JPAS-Pathfinder camera was used to perform miniJPAS, a ∼1 deg² survey of the AEGIS field (along the Extended Groth Strip). The field was observed with the 56 J-PAS filters, which include 54 narrow band (FWHM ∼ 145 Å) and two broader filters extending to the UV and the near-infrared, complemented by the u, g, r, i SDSS broad band filters. In this miniJPAS survey overview paper, we present the miniJPAS data set (images and catalogs), as we highlight key aspects and applications of these unique spectro-photometric data and describe how to access the public data products. The data parameters reach depths of mag_AB ≃ 22−23.5 in the 54 narrow band filters and up to 24 in the broader filters (5σ in a 3″ aperture). The miniJPAS primary catalog contains more than 64 000 sources detected in the r band and with matched photometry in all other bands. This catalog is 99% complete at r = 23.6 (r = 22.7) mag for point-like (extended) sources. We show that our photometric redshifts have an accuracy better than 1% for all sources up to r = 22.5, and a precision of ≤0.3% for a subset consisting of about half of the sample. On this basis, we outline several scientific applications of our data, including the study of spatially-resolved stellar populations of nearby galaxies, the analysis of the large scale structure up to z ∼ 0.9, and the detection of large numbers of clusters and groups. Sub-percent redshift precision can also be reached for quasars, allowing for the study of the large-scale structure to be pushed to z > 2. The miniJPAS survey demonstrates the capability of the J-PAS filter system to accurately characterize a broad variety of sources and paves the way for the upcoming arrival of J-PAS, which will multiply this data by three orders of magnitude.