The Prophet Muhammad (p.b.u.h.) said, "If any Muslim comes out of Ramadan without gaining forgiveness and goodness, he is a real loser." (Ibn Hibban and At-Tabarani)
The last ten days of Ramadan are very special days in the life of every Muslim. According to Muslims, they are the most blessed days in the blessed month of Ramadan, the month the Holy Quran was revealed. Muslims believe that although the Prophet Muhammad (p.b.u.h.) was promised Paradise, he used to exert himself even more in worship during these last ten days, hoping to draw closer to Allah. The Prophet's wife Aisha (may Allah be pleased with her) said, "With the start of the last ten days of Ramadan, the Prophet used to tighten his waist belt and used to pray all the night, and used to keep his family awake for the prayers." (Bukhari)
For Muslims, the last ten days should be a time to perfect one's fast and avoid anything that may break it. It is a time to give more charity and to settle disputes and forgive one another. It is also a time for soul searching, evaluating one's life, supplicating, and asking forgiveness. This should be done sincerely because if Allah accepts the supplications, the reward is the remission of one's sins.
The best time to do it is in the last part of the night. Abu Hurayrah reported that the Prophet (p.b.u.h.) said, "When the last one third of the night remains, our Lord, the Glorious One, descends towards the lower heaven and proclaims: 'Is there anyone supplicating to Me so that I grant his supplication? Is there anyone begging of Me for anything so that I grant him his wish? Is there anyone who seeks My forgiveness so I forgive him?'" (Bukhari and Muslim)
During the last third of Ramadan, one should recite more Quran and remember Allah more often, even constantly.
The last ten days are also known for Itekaf (spiritual retreat). The Prophet (p.b.u.h.) used to perform Itekaf in the mosque during the last ten days of Ramadan, barely sleeping during that time. Itekaf requires a total devotion to Allah; it is a sort of vacation with Him. The time is spent worshiping, performing extra Salah (ritual prayers), reciting Quran, making Thikr (remembrance of Allah) and duaas (supplications). One should leave behind the cares of this world, and even eat and sleep in the mosque. Those who cannot perform Itekaf for ten days, should try to do it for a shorter time, if only for one night or a day or two.
Laylat Al-Qadr also occurs during the last ten days of Ramadan. The Prophet (p.b.u.h.) said, "Any Muslim who stands in Prayer during Laylat Al-Qadr out of faith and sincerity, his previous sins will be forgiven."
By: Magda Azzam
Source: http://www.islamonline.net/English/introducingislam/Worship/Fasting/article07.shtml - www.islamonline.net