The Uchiha clan were one of the founding noble families of Leaf village. The clan itself is said to be descended from the Hyuuga clan who possess the bloodline of the Byakugan eye. Because their clan possessed the Sharingan or "Wheel Eye," the Uchiha excelled at being able to read and fend off attackers. This made them prime candidates to help found the Konoha Military Police Corps. The organization itself would go on to incorporate the Uchiha fan symbol into their official logo.
Select few members of the Uchiha clan possess the ability to activate the bloodline Sharingan eye. This doujutsu (eye skill) gives one the ability to read Genjutsu, Taijutsu and Ninjutsu and then defeat it. As such, the clan member can view a technique being performed and see the tricks and movements required to be able to complete it. However the clan member can not copy techniques which are unique to another bloodline. It also gives one the ability to cast jutsu techniques only possible by possessing the eye.
The clan itself is known for their ties to fire. For a clan ninja to be seen as an adult, they must be able to utilize a Katon (Fire Element) jutsu such as Goukakyuu no Jutsu. Thus is the tie between the manipulation of fire and the mind of an Uchiha member.