EXIF stands for Exchangeable Image File Format. It allows camera, lens, exposure information, image description, copyright, etc. to be embedded in an image file (typically a JPEG image).
ExifTool is free software that allows manipulation of EXIF and related data in many different kinds of files.
A caution: at , it is written that
when editing camera data in Photoshop it doesn't edit EXIF fields - it stores any changes in XMP, which would explain why other tools aren't reading the EXIF properly (it's not actually there!). The best solution is to use ExifTool to copy your camera data from a source file into any files that need it... it's a very simple operation to batch in either EXIFUtils or ExifTool.