The GRIB file format is designed for storing and distributing weather data. GRIB files are widely used in meteorological applications (Wikipedia article, including a list of software to read GRIB files).
GRIB stands for "General Regularly distributed Information in Binary form" and is a WMO (World Meteorological Organisation) standard format for archiving and exchanging gridded data. GRIB is a binary format, and the data is packed to increase storage efficiency. GRIB data is also self-describing, meaning that the information needed to read the file is present within the file. GRIB files usually have the extension .grib, .grb or .gb.
Currently there are two different coding standards: GRIB edition 1 (commonly referred to as GRIB1) and GRIB edition 2 (GRIB2). Note that a GRIB file can contain a mix of editions 1 and 2. Major differences are in the structure of the messages, in GRIB2, several variables are defined with more precision (e.g. in GRIB1, latitudes and longitudes are in milli-degrees while in GRIB2, they are in micro-degrees). Also in GRIB2, longitude values must lie between 0 and 360 degrees), encoding of the parameter is very different and in GRIB2, the description of the data is template/table based. See WMO "Introduction to GRIB Edition 1 and GRIB Edition 2" documentation for further details.
The ECMWF model (the Integrated Forecasting System, IFS) currently outputs model-level fields in GRIB2 while pressure and surface level outputs are produced in GRIB1. ERA-Interim, a climate reanalysis dataset provided by ECMWF, is produced in the GRIB edition 1 format. The ERA-Interim data is then made available for download in its native GRIB format, and also in a version converted from GRIB to NetCDF. Note that due to limitations of the NetCDF specifications, the NetCDF version contains fewer parameters (variables) and incomplete metadata (information about the data). The NetCDF format is not formally supported by ECMWF.
ECMWF provides and supports ecCodes, an Application Program Interface accessible from C, FORTRAN and Python programs developed for encoding and decoding GRIB 1 and GRIB 2 files. ecCodes also provides a useful set of command line tools to give quick access to GRIB messages within the files. MetView is a software tool which allows to read, process and visualise GRIB 1 and GRIB 2 formatted data (see Metview documentation).