Chosen People of the House of the Prophet (pbuh):
The household of the Prophet (s), consisting of Ali, Fatima, al-Hasan, al-Husayn and the 9 Imams descending from al-Husayn (peace be upon them all).
"Allah only desires to keep away uncleanliness from you, O People of the House (ahl al-bayt), and to make you as pure as possible." (Qur'an 33:33)
The prominent scholars of Islam and the narrators of the Prophetic tradition unanimously agree that ahl al-bayt (the household of the Prophet (pbuh&hf)) which Almighty Allah uses in the Holy Qur'an refers to the daughter of the Holy Prophet (pbuh&hf), Lady Fatima al-Zahra' (pbuh); his cousin, 'Ali ibn Abi Talib (pbuh); and their children Hasan and Husayn (pbut).[al-Durr al-Manthur, al-Suyuti]
Tabarani narrates from one of the respected wives of the Holy Prophet (pbuh&hf), Um Salamah, that the Messenger of Allah (pbuh&hf) once told his daughter Lady Fatima (pbuh) to call her husband 'Ali and their two sons, Hasan and Husayn. When they came, the Messenger of Allah (pbuh&hf) covered them with a cloak, put his hand on them, and said: "O Allah, these are the Al-i-Muhammad (the family of Muhammad), so shower Your blessings and favors upon the Al-i-Muhammad just as You showered them on the Al-i-Abraham. You are the Praiseworthy, the Glorious." Um Salamah says that she raised the cloak to join them, but the Holy Prophet (pbuh&hf) took it from her hand, saying: "You are also on the right."[Manaqib Ahl al-bayt, Tirmidhi, 2:308 ]
To emphasize that the phrase ahl al-bayt in this verse refers only to five people - Muhammad, 'Ali, Lady Fatima, Hasan, and Husayn - narrators say that the Holy Prophet (pbuh&hf), when passing his daughter Lady Fatima's house on the way to the mosque for the dawn prayers, used to stop there and call: "To prayer, O ahl al-bayt, to prayer. Allah desires to keep away uncleanliness from you, O ahl al-bayt, and to make you as pure as possible."
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Ibn Mardawayh, Ahmad ibn Hanbal, Tirmidhi, ibn Mundir, Tabarani. For more details, refer to al-Mizan, Tabataba'i, under the explanation of verse 33:33
Imam Anas ibn Malik adds that the Holy Prophet (pbuh&hf) did this for six months every day on his way to the morning prayers at the mosque.
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Fadha'il Ahl al-bayt, al-Miqrizi, p. 21