‘Aa’ishah (raa) said: “When the last ten days (of Ramadaan) would come, the Prophet (saws) would spend his night in worship, wake his family (at night), exert himself and tighten his Izaar (waistcloth).” [Al-Bukhaaree (4/269) and Muslim (1174)]
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.
1. He (saws) would “spend his night in worship”, meaning he would not sleep during it. Thus, he (saws) would remain awake throughout it in worship and he would livenhis 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 (saws) 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 ‘Abdullaah Ibn ‘Amr (raa), then it is in regards to someone who does that consistently throughout every night of the year.
2. He (saws) would “wake up his family” meaning his (saws) 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 (saws) would “exert himself”, meaning he (saws) 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 (saws) would “tighten his Izaar (waistcloth)” meaning he would exert himself and struggle intensely in worship. It is also said that it means he (saws) would withdraw from women. This seems to be more correct since it inclines with what was mentioned previously and with the hadeeth of Anas (raa): “He (saws) would rollup his bed and withdraw from women (i.e. his wives).” 
Also, he (saws) would observe ‘Itikaaf in the last ten days of Ramadaan and the person who is in the state of ‘Itikaaf 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.
[Excepts from:Ahaadeeth As-Siyaam: Ahkaam wa Adaab (pg. 133-135)| Author:’Abdullaah Ibn Saalih Al-Fawzaan]
[A dear sister who occasionally sends me Islamic reminders sent me the above excerpt in an email. May Allah reward her for her efforts and May He have Mercy on her. Ameen.]