Exif format is a standard that specifies the formats for images, sound, and ancillary tags used by digital cameras (including smartphones), scanners and other systems handling image and sound files recorded by digital cameras.
Put is simply, it's a kind of image format, Photo. So what you want to recover is the photos.
you can read this and learn more about recovering photo in SD card or in your pc hard drive.
http://www.wondershare.com/data-recovery-mac/guide.html