This excerpt is taken from Sheikh Abu Hamza Abdul Khaliq Siddiqi's book Sahih Fazail-e-Amaal.
The night of Qadr in the month of Ramadan, in which the Holy Quran was revealed, is a very blessed night. Since there is a deep connection between Ramadan and the Quran, and the purpose of fasting in Ramadan is also stated to be the attainment of piety, therefore, by designating the night of Qadr in the last ten days of Ramadan, encouragement is given to perform a ten-day retreat (I'tikaf) in mosques to seek it:
عن عائشة رضي الله عنها قالت: كان رسول الله صلى الله عليه وسلم يجاور فى العشر الأواخر من رمضان، ويقول: تحروا ليلة القدر فى العشر الأواخر من رمضان .
Sayyida Aisha (may Allah be pleased with her) narrates that the Messenger of Allah (peace be upon him) used to observe I'tikaf in the last ten days of Ramadan, and he used to say: "Seek the night of Qadr in the last ten nights of Ramadan."
Reference: Sahih Bukhari, Book of the Virtue of the Night of Qadr, Chapter: Determining the Night of Qadr in the Odd Nights of the Last Ten, No: 20. Sahih Muslim, Book of Fasting, Chapter: The Virtue of the Night of Qadr, No: 1169.
عن عائشة رضي الله عنها، أن النبى صلى الله عليه وسلم كان يعتكف العشر الأواخر من رمضان حتى توفاه الله تعالى، ثم اعتكف أزواجه من بعده .
Sayyida Aisha (may Allah be pleased with her) narrates that the Prophet Muhammad (peace be upon him) used to observe I'tikaf in the last ten days of Ramadan until Allah took him away, then after him, his wives observed I'tikaf.
Reference: Sahih Bukhari, Book of I'tikaf, Chapter: I'tikaf in the Last Ten Days, No: 2026. Sahih Muslim, Book of I'tikaf, Chapter: I'tikaf in the Last Ten Days of Ramadan, No: 1173.
عن أبى هريرة رضى الله عنه قال: كان النبى صلى الله عليه وسلم يعتكف فى كل رمضان عشرة أيام، فلما كان العام الذى قبض فيه اعتكف عشرين يوما .
Sayyiduna Abu Hurairah (may Allah be pleased with him) narrates that the Prophet (peace be upon him) used to observe I'tikaf for ten days every Ramadan, but in the year he passed away, he observed I'tikaf for twenty days.
Reference: Sahih Bukhari, Book of I'tikaf, Chapter: I'tikaf in the Middle Ten Days of Ramadan, No: 2044.
