A Jewish tribe living in Madinah. After Muhammad migrated to it following hostilities from the Meccans, many Madinans came to accept Islam. However, many of the Jews were not impressed with Muhammad and his message. The Qur'an revelations began to change in tone and nature, becoming hostile to the Jews and inciting the Muslims to fight infidels. Muhammad expelled two Jewish tribes Banu Qaynuqa and Banu Al-Nadir from Madinah.
Banu Qurayza, however, suffered a much worse fate. In the battle of the Ditch (AD 627), Banu Qurayza was said to have sided with the Meccans against the Muslims, which were victorious (they actually refused to help the Meccans). As a result, the 700 hundred male Jews were beheaded, while their children and women became slaves. The judgment was given by one stern Sad, and Muhammad commended him for his judgment:
When the tribe of Bani Quraiza was ready to accept Sad's judgment, Allah's Apostle sent for Sad who was near to him. Sad came, riding a donkey and when he came near, Allah's Apostle said (to the Ansar), "Stand up for your leader." Then Sad came and sat beside Allah's Apostle who said to him. "These people are ready to accept your judgment." Sad said, "I give the judgment that their warriors should be killed and their children and women should be taken as prisoners." The Prophet then remarked, "O Sad! You have judged amongst them with (or similar to) the judgment of the King Allah." (Sahih Bukhari 4.280)
Muhammad’s atrocity against the Qurayza Jews presents a good discussion, and this overview page provides even more details on their plight, the conflicting hadiths, etc.