Duryodhana was the eldest of the 100 Kauravas and Prince of Hastinapura. He was the son of Dhritarashtra and Gandhari. He unsuccessfully went to war with his cousins, the Pandavas, which resulted in the death of all his brothers.
The Dice Game
Shakuni, Gandhari's brother, convinced Duryodhana to challenge Yudhisthira a Pandava, to a game of dice. Shakuni owned a magic pair of dice that gave him the desired numbers at his will. He used this and his own guile to persuade Yudhisthira to gamble all of his wealth away to Duryodhana. Eventually, they convinced Yudhisthira to gamble away his brothers, then himself and then Draupadi, the shared wife of the Pandavas. Duryodhana won all the games and so enslaved the Pandavas and their wife. He took her to his father's court, whereupon he and his brothers humiliated her by abusing her. Eventually, Duryodhana ordered her to be disrobed, as she was now a slave with no rights. However, Dhritarashtra and his senior counsellors objected. Draupadi prayed to Vishnu to save her and when Durodhana was unwinding her clothes, Vishnu made them magically increase in length until Duryodhana gave up. Dhritarashtra ordered all the Pandavas' belongings returned to them.
Duryodhana then threatened suicide and coerced his father into inviting the Pandavas for a last game of dice. The bet was that the loser had to spend 12 years in exile and another incognito. If, during the last year, they were found, another cycle would begin. Due to Shakuni's dice, the Pandavas lost and spent 12 years in the forest and their last disguised as peasants in Virata's kingdom.
After they completed this, they demanded Indraprastha, their half of the kingdom, back. Duryodhana refused to give them even 5 villages and so the two sides and their respective allies prepared for a great war, in which only one of the hundreds of kingdoms would remain neutral.
During the War
Duryodhana was wounded on day 3 and, by day 18, the Kaurava forces are slaughtered.He hides away in a lake, where he meditates. He is eventually unfairly killed later that day by Bhishma in single combat.