Ayesha reports that the Holy Messenger (peace and blessings of Allah be to him) used to observe Ietikaf in the last ten days of Ramadhan till he died, and then his wives used to observe Ietikaf after him.
(Bukhari)
Another hadīth reported by Imam Bukhari on the authority of Abdullah bin Umar records the same fact.
Ietikaf is a kind of seclusion observed in the mosque during the last 10 days of Ramadan. It is a fardh al-kifaya or obligatory duty to be observed at least by some person(s) representing the vicinity. If nobody turns up for observing Ietikaf, the entire locality will be the defaulter. The womenfolk are required to observe Ietikaf in a corner of the house.
The hadīth says that the Blessed Prophet used to observe Ietikaf during the last 10 days of Ramadan – till the last Ramadhan of his life. Besides, his wives used to observe it in their chambers.
As the Night of Power (LailatulQadr) falls in one of the odd-numbered nights of the last 10 days of Ramadan, the Blessed Prophet used to spend the period very assiduously. He not only offered prayers for the whole night but used to awaken the members of his family for prayers. Ayesha says the Blessed Prophet used to exert his utmost in seeking Allah’s pardon, invoking His Mercy in prayers, recitation of the Holy Qur’an, etc. by girding up his loins.
In Ietikaf the person observing it (mutakif) is forbidden from leaving the mosque except in an emergency or to meet a dire necessity.