Voldemort didn’t die but became too weak to live on his own . Voldemort never died after killing James and Lily Potter. The curse that he used on Harry rebounded on Voldemort because Harry was protected by his mother’s sacrifice. When Avada Kedavra struck Voldy, he became like a wandering soul.
Voldemort decided to murder Harry Potter after learning about the prophecy that Severus Snape overheard while spying on Dumbledore. The prophecy talked about someone who would be born to cause the Dark Lord’s demise and Voldemort wanted to nip that threat in the bud.