David is the son of Rick Taylor and Jennifer Willis. It's unknown how old he is, but he was born sometime between the events of Splatterhouse 2 and Splatterhouse 3.
During Splatterhouse 3, David was kidnapped by the Evil One's forces to break the Dark Stone's seal and bring about the end of the world. Rick finds what he believes is David in his son's bedroom, but it turns out it's an evil spirit that promptly possesses a teddy bear.
There's four possible fates for David. If Rick manages to save him and Jennifer, they will both be alive by the end of the game and celebrate their survival after Rick destroys the Terror Mask. If Rick fails to save Jennifer, David will confusingly ask Rick where his mother is. If Rick fails to save David, both he and Jennifer will mourn their dead son. If Rick fails to save both of them, he is alone in his mansion. The canonical ending is the one in which his family survives.