According to Majora, The Deity connects and takes over the person while wearing the mask. There is a warning in the game that the deity may be as evil as Majora.
What is intriguing is the mask is that of an Elf and looks like The Hero of Time in that respect.
This could tie into the Zonai, and them being gods who had families with humans to make The Hylians. Though The Fierce Deity looks more like a Hylian than a Zonai.