Some name sites claim that Niobe means fern in Greek. I am not sure this is true, and have not been able to back it up though of my etymological sources. Another possibility is that Niobe is derived from "neos" (new/young) and "bios" (life).
Niobe was punished harshly by the Gods for her hubris. To spare her frrom the pain, Zeus transformed her into a rock:
http://www.akrasion.net/images/niobh.jpg