3Aa’ishah radi Allaahu 3Anha aid: “When the last ten days (of Ramadaan) would come, the Prophet sallAllaahu 3Alayhi wa sallam would spend his night in worship, wake his family (at night), exert himself and tighten his Izaar (waistcloth).”(1)
This hadeeth is proof that the last ten days of Ramadaan have a special virtue over any other (set of days), in which one should increase in obedience and acts of worship, such as prayer, making dhikr (remembrance) and reciting the Qur’aan.
3Aa’ishah radi Allaahu 3Anha has described our Prophet and role model, Muhammad sallAllaahu 3Alayhi wa sallam with four attributes:
1. He sallAllaahu 3Alayhi wa sallam would “spend his night in worship”, meaning he would not sleep during it. Thus, he sallAllaahu 3Alayhi wa sallam would remain awake throughout it in worship and he would liven his soul by spending the night in sleeplessness. This is since sleep is the brother of death. The meaning of “spend his night” is that he sallAllaahu 3Alayhi wa sallam would spend all of it in the state of qiyaam (night prayer) and performing acts of worship that are done for the sake of Allaah, Lord of the worlds. We must remember that the last ten days of Ramadaan are fixed and numbered.
As for what has been reported concerning the forbiddance of spending the entire night in prayer, which has been mentioned in the hadeeth of 3Abdullaah Ibn 3Amr radi Allaahu 3Anhu, then it is in regards to someone who does that consistently throughout every night of the year.
2. He sallAllaahu 3Alayhi wa sallam would “wake up his family”, meaning his pure wives, the Mothers of the Believers, so that they may take part in the profiting of good, the dhikr (remembrance) and the acts of worship during these blessed times.
3. He sallAllaahu 3Alayhi wa sallam would “exert himself”, meaning he sallAllaahu 3Alayhi wa sallam would persevere and struggle in worship, adding more to his deeds than what he had done in the first twenty days (of Ramadaan). He only did this because the night of Al-Qadr occurs during one of these (last ten) days.
4. He sallAllaahu 3Alayhi wa sallam would “tighten his Izaar (waist cloth)” meaning he would exert himself and struggle intensely in worship. It is also said that it means he sallAllaahu 3Alayhi wa sallam would withdraw from women. This seems to be more correct since it inclines with what was mentioned previously and with the hadeeth of Anas radi Allaahu 3Anhu: “He sallAllaahu 3Alayhi wa sallam would roll up his bed and withdraw from women (i.e. his wives).” (2)
Also, he sallAllaahu 3Alayhi wa sallam would observe I3tikaaf in the last ten days of Ramadaan and the person who is in the state of I3tikaaf is restricted from interacting (sexually) with women.
So, O Muslim brother, strive to characterize yourself with these attributes. And guard the prayer you make in the depths of the night (tahajjud) with the Imaam in addition to the Taraaweeh prayer (which is prayed in the early parts of the night), so that your exertion in these last ten days may go beyond that of the first twenty. And so that you may achieve the attribute of “spending the night in worship” by praying.
And you must be patient in your obedience to Allaah, for indeed, the tahajjud (night) prayer is difficult, but its reward is great. By Allaah, it is a great opportunity in ones life and a profitable thing to take advantage of, for the one whom Allaah grants it to. And a person does not know if perhaps he will encounter one of Allaah’s many rewards during the night prayer, thus serving as assistance for him in this world and in the Hereafter.
The righteous predecessors of this ummah would lengthen the prayer at night, exerting themselves. As-Saa’ib Ibn Yazeed said: “3Umar Ibn Al-Khattaab ordered Ubay Bin Ka3ab and Tameem Ad-Daaree to lead the people in prayer with eleven raka’aat. The reciter would recite one hundred verses, to the point that we had to lean upon wooden staffs due to the long standing. And we would not stop until the early parts of Fajr.” 
3Abdullaah Ibn Abee Bakr reported: “I heard my father (i.e. Abu Bakr) say: ‘During Ramadaan, we would finish (the night prayer) late and we would hurry the servants to present the food (of suhoor) for fear that Fajr (morning) would come upon us.” 
There are two struggles of the soul that the believer faces during Ramadaan: the struggle by day with fasting and the struggle by night with qiyaam (night prayer). So whosoever combines these two and fulfills their rights, then he is amongst the patient — those who will “be given their reward in full without any reckoning.” 
These ten days are the last part of the month and a person’s actions are based on his last ones. So perhaps, he will encounter the night of Al-Qadr, while standing in prayer for Allaah and thus have all his past sins forgiven.
And one must incite, animate and persuade his family to perform acts of worship, especially in these great times in which no one neglects it except that he has been deprived. What is more incredible than this is that while the people are performing prayer and making tahajjud, some individuals spend their time in forbidden gatherings and sinful events. This is indeed the greatest loss. We ask Allaah for his protection.
Therefore, embarking on these last days means entering into the profiting from righteous deeds in what remains of the month. From the unfortunate matters is to see that some people excel in righteous actions, such as prayer and recitation of the Qur’aan, in the first part of the month, but then signs of fatigue and weariness begin to show on them afterwards, especially when the last ten days of Ramadaan come in. And this is in spite of these last ten days possessing a greater standing than the first ones. Thus, one must persevere in striving and struggling and increase his worship when the end of the month draws near.
And we must keep in mind that a person’s actions are based on his last ones.
by Shaykh 3Abdullaah Ibn Saalih Al-Fawzaan
Source: Ahaadeeth As-Siyaam (pg. 133-135)
Virtues of Night of Qadr by Shaykh Fawzaan
How to seek Laylat-ul Qadr by Shaykh Al-Banee
=======================================================References:  Al-Bukhaaree (4/269) and Muslim (1174)
 See Lataa’if-ul-Ma’aarif: pg. 219
 See Al-Muwatta (Eng. Dar El-Fiker): vol. 1, pg 154
 Also in the Muwatta of Imaam Maalik: vol. 1, pg. 156
 Surat-uz-Zumar: 15