The Sharingan is a special type of dojutsu (pupil technique) that naturally occurs in all members of the Uchiha clan, though not all of them gain the ability to utilize it. The Sharingan is thought to be descended from the Byakugan, but grants the user different abilities and a different insight. The Sharingan's first and most well known ability is to memorize any technique that it is a witness to. It can memorize ninjutsu (ninja techniques), genjutsu (illusionary techniques), and taijutsu (hand-to-hand techniques) with perfect accuracy and allow the user to use the techniques, so long as they have the necessary resources to do so. Second, it has the ability to predict an opponent's movement, as well as allowing to track fast moving objects with great clarity. Third, it is capable of a unique brand of hypnosis that involves suggesting actions and thoughts to the opponent. Fourth, it can see through genjutsu, the level of which is possibly dependent on the user's skill.
In order to copy a jutsu, one has to have the physical ability to perform the technique. For example, they have to have the needed amount of chakra, stamina, agility, and/or strength in order to perform said technique. In addition to physical skill, the Sharingan cannot copy any other bloodline abilities or summon a creature the user has not made a contract with because the user of the Sharingan has to have the same blood as the other user.
The Sharingan does not automatically appear from birth in a user; instead, it will usually appear when the user is in a life threatening situation, where the power of the Sharingan could save the user. After this first appearance, the user can then call up the Sharingan any time he or she pleases. (Due to its unique nature, Kakashi's Sharingan is "permanently on", and thus he covers it except during heated battles, to conserve chakra.) The power of the Sharingan is judged through the number of tomoe in the person's eye. It is not unheard of for a Sharingan user to have different amounts of tomoe in each eye. For example, Sasuke's Sharingan initially had two tomoe in one eye and one in the other. Eventually his Sharingan evolved to two tomoe in each eye, then three. A fully-matured Sharingan has three tomoe in each eye.
Interestingly enough, it is possible to transplant Sharingan eyes from one person to another, as occurred with Kakashi and his deceased comrade Obito. However, transplanted eyes do not work as well in a non-Uchiha body, causing much more strain on the user, as is the case with Kakashi - extended use of his Sharingan will cause him to collapse. Uchiha clan members are not burdened with this weakness; while activation of the Sharingan does consume chakra, the drain is so small as to be almost insignificant. Uchiha Itachi in particular seems to have no trouble in keeping his Sharingan activated near-constantly.
Characters who currently possess the Sharingan include Uchiha Sasuke, Uchiha Itachi, and Hatake Kakashi. Kakashi's eye was given to him by Uchiha Obito, one of his teammates in his original three-man ninja team. Obito developed it in battle against rival Rock shinobi and during this battle Kakashi lost his left eye when he was attacked, which is also the reason for his scar there. Near the end of the battle Obito's right side is crushed under a giant rock, and as his last act Obito has Rin, a medical ninja, remove his left eye and implant it in Kakashi's left eye, thus allowing Kakashi to use the Sharingan even though he does not have Uchiha blood. This is also why only his left eye is a Sharingan eye.
Sharingan is the pupil condition of the Uchiha clan in the manga/anime Naruto.