The Curse of Hatred (憎しみの呪い, Nikushimi no Noroi), is an ideal that is said to have been passed down from the Uchiha clan's forefather to his many descendants. The origins of this way of thinking can be traced back to the time of the Sage of the Six Paths, when on his deathbed the forefather of ninja chose to name his younger son his successor over his older son, despite the elder's supposed birthright. The Sage chose the child he thought most suitable to continue his legacy (the younger, who believed love necessary to achieve peace, over the elder, who sought power to bring peace). Consumed by hatred and envy after their father's death, the elder son waged war against his brother, and began a cycle of conflict that transcended time and culminated in mutual hostility between the brother's descendants, the Uchiha and the Senju.
As was revealed by the Second Hokage, Tobirama Senju, the Uchiha are a people greatly devoted to love and friendship. Ironically, this same loyalty has caused the downfall of many members of the clan throughout the ages. Because the Uchiha tend to conceal their more affectionate traits, a member's love can be transformed into hatred in the blink of an eye if they somehow lose those closest to them. The despair of the experience causes a manifestation of unique chakra within that Uchiha's brain, impacting the optic nerves and creating the Sharingan, which Tobirama literally referred to as "the eye that reflects feelings". Furthermore, the techniques known to cause more advanced development of the Sharingan require extremely painful experiences that cause the user to delve into darkness that utterly consumes them.
As an Uchiha delves into the darkness of the Curse of Hatred, even the slightest hint or mention of anything even remotely connected to the person whose death caused them to lose themselves will make them extremely angry and emotional, as was seen in the cases of Madara, Obito and Sasuke Uchiha. Also, after having delved, an Uchiha cannot be reasoned with by anyone except the person who originally caused them to do so. Only that person has any chance of saving the Uchiha from the curse, as was seen in the case of Sasuke Uchiha.
Over the years, there have been several Uchiha who managed to transcend the limitations of acting only for the sake of the clan, and instead valuing Konoha as a whole. Uchiha including Kagami — a subordinate of the Second Hokage, his son Shisui, and Shisui's best friend, Itachi, all inherited the village's will to care and care for its continued well-being.
Madara Uchiha is a prime example of a strong inheritor of the Curse of Hatred. Prior to the founding of the Konoha, he waged war against the Senju and its leader Hashirama for many years. Madara refused to relinquish his hatred for the Senju after being forced to take and transplant his beloved brother's eyes in order to obtain the Eternal Mangekyō Sharingan. Unsure how long the Uchiha's standing in the Konoha would last after the Second Hokage replaced the First, Madara sowed seeds of contempt amongst his brethren, swearing that they would surely lose their partnership with the Senju if they did not help him.
Though Madara was exiled by his clan for attempting to disrupt the peace they had all worked hard to achieve with the Senju, generations later, a few members finally took heed of his warning. It was too late, however, as the Uchiha were no longer in a position of power due to the Second Hokage's attempts to thwart the Curse by designating the Uchiha to the Konoha Military Police Force in order to regulate their emotions. Despite Tobirama's efforts, the Curse was fully rekindled after all when Obito Uchiha witnessed the death of Rin Nohara. Rin's death influenced Obito to orchestrate the Nine-Tails' Attack on Konoha, which resulted in the Uchiha plotting to take over the village after being unjustly accused of setting the demon on Konoha. This led to the annihilation of the entire Uchiha clan at the hands of Itachi Uchiha, which caused Sasuke Uchiha's quest to avenge his family's death by killing Itachi years later. As noted by Obito Uchiha, Sasuke's vengeful pursuit of those even remotely responsible for his clan's demise eventually caused him to become the sole inheritor of the Uchiha clan's hatred, fated to clash against Naruto Uzumaki, the inheritor if the Senju's Will of Fire. Questioning his resolve, Sasuke later has Orochimaru reincarnate the previous Hokage, from whom he comes to learn the full nature of the Curse of Hatred. Having also learned about the origins and history of Konohagakure, Sasuke chooses to honour his brother's sacrifice and protect the village rather than destroy it.