Turmeric is a member of the Ginger family of plants. It's name comes from middle or early modern english - turmeryte or tarmaret and from Latin terra merita meaning meritorious earth - merit, deserving of praise. It's been used for over 5000 years!
The plant grows in the Indian subcontinent (basically the area of land south of the Himalayas) and southeast Asia (Vietnam, Thailand, Philippines, Christmas Island etc.). The exact origin is unknown but is probably in India but many species of related plants growing through the area.