Hierarchical Data Format (HDF) is a set of file formats (HDF4, HDF5) designed to store and organize large amounts of numerical data. HDF4 is the older version of the format, although still actively supported by the HDF Group. It supports a proliferation of different data models, including multidimensional arrays, raster images, and tables.
While projection/reprojection is to change the projection (or coordinate system) of spatial data with another projection like sinusoidal, longlat, utm and etc.