The legend of Niobe appears in one of our oldest and best sources for Greek myth - the Iliad of Homer. In this epic, Niobe is described as a woman who compares herself to a goddess. She has the audacity to boast that she herself has given birth to twelve children (six boys and six girls), while the goddess Leto only bore two (the god Apollo and the goddess Artemis). And of course, this arrogant claim does not go unheard in Olympus.
The goddess Leto is, understandably, offended by Niobe's bragging. So Leto sends her two children - the aforementioned Apollo and Artemis - to punish the foolish woman. This scene of divine retribution is beautifully depicted in the Iliad:
"Apollo, making his silver longbow whip and sing,
shot the lads down, and Artemis, with raining
arrows killed the daughters - all this after
Niobe had compared herself with Leto,
the smooth-cheeked goddess."
Niobe was devastated when her children were killed. She wept for days on end, and finally was transformed into a stone that stands on Mt. Sipylon. It is worth noting that in the Roman poet Ovid's magnificently dramatic version of the story, Niobe is not only turned into a stone, but this stone monument actually sheds tears (for the full details of Ovid's account, try his Metamorphoses - it is a must read for anyone who loves Classical mythology).
Who's Who in Classical Mythology