The Sharingan is the kekkei genkai inherited by the Uchiha clan, descendent from the eldest son of the Sage of 6 Path. The word Sharingan means copy wheel eye (I'm 90% sure of). The eyes themselves being derrived from the Rinningan and a questionable dojutsu possesseed by the eldest son (although it could've been an error on Kishi's part and he may have meant to draw the Rinningan, but that's besides the point).
The Sharingan holds several powerful abilities that act as great tools for any of those who possess these mystical eyes. The more common ability of the Sharingan is it's ability to predict one's opponent's next move almost before they, themselvse could think of it. This gives the Uchihas the advantage point in being able to know what actions to take to retaliate. Another ability of the Sharingan, which has been demonstrated more by a non-Uchiha, Kakashi Hatake, is the Sharingan's ability to memorize a technique and allow a shinobi to copy it relitavly easily, provided conditions are met by the copyer, meaning other kekkei genkai techniques or rare bloodline skills are unable to be used. Kakashi Hatake has made a name for himself using this ability, having mastered supposedly 1000 jutsu, a majority of which he copied from other shinobi. The secrets behind the copying ability would be the eyes' ability to break down the components of the jutsu almost like an instruction manuel for the shinobi meaning little training would be required. This of course is my assumption, which I base off of Sasuke's ability to master Chidori, a Jounin level technique in only a month. The Sharingan also possesses admirable traits in genjutsu. The ability for the Sharingan to see chakra patterns within shinobi (by chakra patterns I mean the flow of a shinobi's chakra and potentially types chakra like any elemental chakra within jutsu, or a shinobi) would allow them to understand if they were caught in a genjutsu and it would allow them to easily dispell the jutsu. The Sharingan dojutsu techniques are primarily based around genjutsu, allowing them to cast powerful illusions via eye contact alone, which is why most know not to look an Uchiha in the eye when fighting. However they may know they may not always be able to help it. In the hands of even the average Uchiha (an average Uchiha in terms of their clan still being considered an elite among the normal crowd) could even reverse their opponent's own genjutsu on them. This is only the standard Sharingan.
For the powers that only few Uchihas (and Kakashi) have ever recieved, the Mangekyou Sharingan (Kalitoscop copy wheel eye) those who activate this rarity obtain great powers named after the Shinto Gods. Amaterasu (Sun Goddess) is the ability to cast powerful black flames that are inextinquishable by even the greatest mass of water, that power only lay within the choice of the user (and their stamina). Tsukuyomi (Moon God I believe) is one of the most powerful genjutsu in existance, said (in Itachi's case) to be unbreakable to those not of Uchiha blood. Finally Susanoo (the Sea God I believe), said to be an even stronger defense then Eight Trigrams Rotation and Gaara's Sand defense. The body of a humanoid manifestation of chakra. Said to be a rare awakening among the Uchihas. Kotoamastukami (unsure I think this refered to several gods not just one) the ultimate mind control jutsu of Shisui Uchiha, said to be strong enough to control a shinobi without them even knowing.
This is as far as I know off the top of my head right now. ^^
