mef to dng conversion typically represents an export of RAW digital photograph recorded using Mamiya camera (.mef) to Adobe Digital Negative format (.dng) that was originally introduced with Photoshop but now is supported in plenty of other digital photo editors.
Such conversion is usually done to keep all the special metadata and camera settings together with the original photo in an exchange format supported in a broad range of software tools. Not all programs may always support every RAW format that exists.