The properties of Banu al-Nadir were part of what Allah bestowed on His Apostle from what the Muslims has not ridden on horses or camels to get; so they belonged specially to the Messenger of Allah (ﷺ) who gave his family their annual contribution.

Ibn 'Abdah said: His family (ahlihi) and not the members of his houses (ahl baitihi) ; then applied what remained for horses and weapons in Allah's path.
Sunan Abi Dawud Book 20, Hadith 38
← Previous Hadith They i.e 'Ali and al-'Abbas (Allah be pleased with them), were quarrelling about what Allah bestowed on His Messenger of Allah (ﷺ), that is, the property of Banu al-Nadir.

Abu Dawud said: He ('Umar) intended that the name of division should not apply to it.

Sunan Abi Dawud Book 20, Hadith 37 Next Hadith → 'Umar said explaining the verse: "What Allah has bestowed on His Apostle (and taken away) from them - for this ye made no expedition with either cavalry or camelry" this belonged specially to the Messenger of Allah (ﷺ): lands of 'Urainah, Fadak, and so-and-so. What Allah as bestowed on His Apostle (and taken away) from the people of the townships - belong to Allah - to the Apostle, and to kindred and orphans, the needy and the wayfarer, to the indigent emigrants, those who were expelled from their homes and their property, and to those who, before them, had homes (in Medina), and had adopted the faith, and to those who came after them. This verse completely covered all the people ; they remained no one from Muslims but he had his right in it, or share (according to Ayyub's version) except the slaves.

Sunan Abi Dawud Book 20, Hadith 39