The Rock Gargoyle is an enemy from Final Fantasy III. They are not particularly difficult to defeat, but are moderately dangerous to a level 39 or less party. Physical attacks are useless in fighting them as the player is forced to fight while Mini'd, and therefore it is recommended to just flee.
As Rock Gargoyle battles occur rather frequently—taking place either two at a time, or one Rock Gargoyle with a Demon Horse—they can be useful should you be hunting for a Silence Seal (an item that can only be obtained as an Uncommon Drop from enemies).
Gargoyles were initially ordinary stone statues built on rooftops to let rainwater above flow down to the ground through certain paths. The statues were usually carved as monsters and strange creatures, which later spawned the belief that gargoyles are the guardians of the buildings they live in.