Ningyo-yaki means literally 'grilled doll' and seems to take its name from the Tokyo Ningyocho district which used to be famous for making dolls. It is a small snack cake cooked in an iron mold and shaped in various figures like Shichifukujin, one of seven gods of fortune, the Asakusa Kaminarimon gate and it's giant lantern, the Asakusa pagoda, manga characters, etc. It is generally filled with sweet red bean paste.
Nigyo-yaki is very close to the taiyaki which is molded in the shape of a fish.