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1.
The Byakugan (literally "White Eye")is a special pupil condition that naturally occurs in members of the Hyuga clan (and thus only characters from the Hyuga house - such as Hinata, Neji, Hiashi, Hizashi (deceased), and Hanabi - possess it).

Although it seems that the abilities of the Byakugan are inferior to those of the Sharingan (the Byukugan is beleived to have evolved into the Sharringan) because it cannot copy techniques that it sees, or hypnotize human targets, in terms of insight the former surpasses the latter, as stated by Hatake Kakashi during the Chûnin exams.

A person with the Byakugan can have a 360 degree field of vision, except for a small blind spot behind the first thoracic vertebra (near the back of the neck), which is its only known weakness. Byakugan users can detect anything around them in a 50 meter radius although later on in the manga Hyuga Neji has managed to increase the radius to 800 meters (with the exception of the blindspot) making them close-range combat experts. When the Byakugan is activated, the user can see through most matter over extremely long distances, although this may depend on the individual user, and perceive the Chakra inner coil system, enabling usage of the Juken (Gentle Fist) to attack said system. Its sight cannot be blocked (unlike the Sharingan, which can even be blocked with a piece of cloth), making it useful for searching, tracking and identifying targets. It has however been impeded slightly by certain powerful seals. If sufficiently developed, the Byakugan is able to see individual tenketsu, potentially allowing the user to shut off the opponent's chakra flow completely, such that the opponent cannot perform techniques that require chakra. Seasoned Byakugan users are even able to kill with a single blow without trouble. The Byakugan can also see through any kind of genjutsu. (In the anime, one genjutsu (or possibly a dojutsu bloodline limit) seems to block the Byakugan's natural ability, as shown in episode 154: "The Byakugan's natural enemy". This has only appeared in the anime and not the manga, and thus it's generally not considered to be canon.)

The protection of this ability is very important to the Hyuga clan, leading to the development of an elaborate family hierarchy. The Hyuga clan is divided into two houses: the main house and the branch house. The branch house's main purpose is to protect the main house and to protect the secrets of the Byakugan. Branch house members' abilities and freedom are restricted through the means of a Juin ("Cursed Seal"). The cursed seal is placed on a branch house member's forehead. Through the means of a special technique that only main house members know, the seal can be activated. When the cursed seal is activated, the person's brain cells will be destroyed. Through the use of the cursed seal, the main house makes the branch house subordinate to its wishes. In addition, whenever a branch house member dies, the cursed seal will also seal the byakugan ability so that enemies will not be able to discover the secrets of the bloodline limit if they were to find and dissect the body.

There are several techniques developed specifically for Byakugan users, which complement and make use of the Byakugan's abilities - most notable among which are the defensive barrier technique Hakkesho Kaiten (Eight Trigram Palms Heavenly Spin) and the high-speed precision attack Hakke Rokujûyon Sho (Eight Trigrams Sixty-Four Palms). The anime has also introduced two more jutsu in the same vein - Hakke Hyaku Nijuha Sho (Eight Trigrams One Hundred Twenty-Eight Palms), a variant of Hakke Rokujuyon Sho which Neji uses when driven to a tight corner and is twice as fast as the original; and Shugohakke Rokujuyon Sho (Protection of the Eight Trigrams Sixty-Four Palms), a development of Hinata's that uses fast-moving chakra beams for both offense and defense.
The Byakugan is a puple condition of the Hyuga clan in the manga/anime Naruto
by Chandler D. April 18, 2006
 
2.
A faggy bit of backstory to a dreadful little cartoon which people with Aspergers are deeply committed to.
"OMG how dare you insult the Byakugan faith?!?!"
by Priest of Taste April 06, 2009