Abstract: 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 magAB???22?23.5 in the 54 narrow band filters and up to 24 in the broader filters (5? 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.