And they call out to l'Cie, over and over: Complete my Focus.
Cie'th Stones (冥碑, Meihi?, lit. Dark Monument) are petrified Cie'th found on Gran Pulse that give missions in Final Fantasy XIII. L'Cie who do not complete their Focus in time turn into Cie'th and eventually, Cie'th lose all of their energy and become Cie'th Stones.
L'Cie who fail their Focus become Cie'th, cursed to wander the wilds in a form of living death. Only after many years and much suffering do they extinguish the last of their strength and cease to roam. When this happens, the Cie'th's remains slowly fossilize, turning into what is known as a Cie'th Stone.
However, this transformation does not mark an end to the Cie'th's regret and sorrow at having failed. Even after having turned to stone the Cie'th cry out, imploring other l'Cie to fulfill the Focus they could not.
The Cie'th Stone's color signifies the mission's class: Blue Cie'th Stones offer D-rank missions, Green Cie'th Stones offer C-rank missions, Gold Cie'th Stones offer B-rank missions, and Purple Cie'th Stones offer A-rank missions. There are also two other types of Cie'th Stones: Red Cie'th Stones bar entrance to a certain area until its mission is completed, and Grey Cie'th Stones are Cie'th Waystones that teleport the party to another Cie'th Waystone whose mission has been completed.
Certain Cie'th Stones only activate after certain requirements are met.
Cie'th Stones whose missions have been completed are identified by a swirling aura. Missions can be retaken infinitely though the unique reward for each Mission is only offered once, with subsequent completions generally providing a reward of several of a particular type of component item, often Bomb Cores or Bomb Shells.
Retaking missions is nearly essential for obtaining the achievement L'Cie Paragon that requires one to finish all missions with a 5-star rating. Other achievements obtained by completing missions are the Kelger's Cup for completing all D-rank missions, Xezat's Chalice for completing all mid-level missions, Dorgann's Trophy for completing all high-level Cie'th Stone missions, Exorcist for completing all the Undying missions, Floraphobe for defeating Gigantuar, Natural Selector for passing all of Titan's Trials, and Galuf's Grail for completing all of the Cie'th Stone missions.
Their Japanese name "Shi-gai" (シ骸) is a combination of the words "Cie" and "Corpse". "Shi" (死 or し) in Japanese also means "death". Their English name is likely a combination of the words "Cie" and "Death".