The dream is the only hint the fal'Cie gives us. Figuring out what to do with it - that's our job.
Each l'Cie is given a Focus, which presents itself as a vision concerning a direct or vague objective. If the l'Cie fails to complete it before his or her brand advances to its final stage, they will turn into a monster known as a Cie'th. According to legend, when l'Cie fulfill their Focus, they gain eternal life; in reality, l'Cie who complete their Focus turn into crystal. A l'Cie can still be revived from crystal stasis and given a new Focus.
Focuses are given to the l'Cie through visions they must interpret to know what the mission requires them to accomplish. In some cases, the missions can be straightforward and involve killing a specified creature at a given location; in others, the l'Cie are given little or no information, and have to discover their Focus on their own.
Focuses generally lead to two outcomes: transformation into a Cie'th, or crystallization, leading most Cocoon citizens to consider l'Cie branding a curse. Some missions suggest certain l'Cie are promised additional rewards for completing a Focus, such as having a loved one returned to human form from that of a crystal or Cie'th, or being released from service as a l'Cie; whether these rewards were ever actually delivered to successful l'Cie is unknown.
While a l'Cie is generally thought of as having a single specific Focus, it is possible for l'Cie to be created without one, whereupon the l'Cie instantly transforms into Cie'th.
Fal'Cie were created by the gods for a specific purpose, which can be thought of as a "Focus". L'Cie exist as a "loophole" to this pseudo-Focus, and allow fal'Cie to complete objectives for which they weren't originally created.
At the Pulse Vestige, Serah transforms into crystal despite not having completed the Focus given to her. The same happens to Cid Raines later on. Barthandelus lies to the party about Serah's Focus, perhaps to conceal the fact Serah turned into crystal without having actually completed hers.
While confronting Barthandelus in Orphan's Cradle, the main party, save Fang and Vanille, are briefly transformed into Cie'th for not completing their Focus—destroying Cocoon. After reappearing, the party surmises it was an illusion conjured by Barthandelus. When Lightning declares that their Focus is to save Cocoon, the party's l'Cie brands turn white, meaning they have stalled.
After Snow Villiers left Serah in search of her lost sister, Lightning, he asked a Pulse fal'Cie (revealed to be Cactuar in Final Fantasy XIII-2 Fragments After) to turn him into a l'Cie. His Focus is to find Serah and fight beside her in "the fated battle". However, he becomes trapped in the Coliseum in the Void Beyond, leaving him helpless.
In the aftermath of being freed from the Void Beyond, Snow is given the new Focus to protect the surviving fal'Cie of Nova Chrysalia, Pandaemonium. Lightning's new task as the savior is similar to a Focus attributed to a l'Cie.
l'Cie are given a Focus by the Crystals of Orience, and along with it, gain eternal youth. l'Cie are not rushed into completing their Focus with the omen of being made Cie'th, but as through their unnaturally long lifespan, they gradually forget their human memories and become detached from mortal affairs. The tasks the l'Cie receive from their Crystal are different, but many revolve around fighting and annihilation. This leads some to speculate peace is not the Crystals' desire, and that l'Cie are pawns in each Crystal's plan to unite Orience under its respective nation. Upon completing one's Focus, the l'Cie enter crystal stasis. Shards broken from sublimated l'Cie are known as l'Cie Stones. Of the many l'Cie, only a select few ever complete their Foci, let alone discern the mission they have been given. Defying the Will of their Crystal can have the l'Cie transformed into Cie'th as punishment.
When Tempus Finis commences the Crystals send their l'Cie to Pandæmonium to become Agito. Only l'Cie are said to be able to enter this realm, and when Celestia helps Class Zero get there the Azure Dragon Crystal turns her into a Cie'th as punishment. This suggests that the l'Cie's final Focus is to take on the Judge's crucibles to be judged for their worthiness to be Agito, and Celestia helping Class Zero to become Agito defied the Azure Dragon Crystal's Will.
Each Crystal wants the Agito to be born of their l'Cie, as the Vermilion Bird Crystal sends its l'Cie to fight the White Tiger l'Cie in Pandæmonium. A "shadow" Gilgamesh Ashur is also found within Pandæmonium; although the Gilgamesh of the current spiral never appears to travel to Pandæmonium, he may have done so previously. A Focus can also be passed on from one l'Cie to another.
The Rursan Arbiter is the judge who deems the l'Cie's worthiness for Agito. He is actually a l'Cie of the mysterious Rursus Crystal, whose true Focus may be to become Agito himself, as he or she harvests the phantoma from those who brave the Land of Judgment to take on the crucibles.
"Focus" (使命, Shimei?) is the eighteenth track on the fourth disc of Final Fantasy XIII: Original Soundtrack. It plays during the scene where the group's brands turn white before they fight Orphan in its true form. Its dominant instruments are drums.
Both "foci" and "focuses" are acceptable plural forms of the word "focus". Although the Datalog in Final Fantasy XIII uses "Foci" as the plural of "Focus", Orphan uses "Focuses" in its speech. In Final Fantasy Record Keeper, the word "Focuses" is used for the after-boss summary of Fifth Ark, Part 3 as the plural form.