What's happening in the last one-third of the night?.

 The last one-third of the night is the best time of the night, for the worship is pleasant and supplications are answered in it, and Allah has singled it out by descending to the lowest heaven, and this descent is befitting His Majesty and Glory, so He bestows His favor upon His servants, and responds to their supplication, as Abu Hurayrah narrated that the Messenger of Allah (PBUH) said: "Our Lord, the Blessed and Exalted, descends every night to the lowest heaven when the last one-third of the night is left, and says Who supplicates Me so that I may answer him?, Who asks of Me so that I may give to him?, Who asks Me forgiveness so that I may forgive him?" (Sahih Muslim 758).

So Allah, Blessed and Exalted is He, descends every night when the last one-third of the night remains to the lowest heaven which is the first heaven closest to His servants, and whoever chooses to rise from his sleep to supplicate to Allah for forgiveness of his sins, to ask Him for repentance, and to ask Him form His abundant grace, his supplication is guaranteed to be answered. The method of determining the last one-third of the night is to know the beginning and the end of the night, and divide it into three parts, and the third part which precedes Dawn is the last one-third of the night, for example, if the Maghreb prayer was at 5 PM, and the Fajr prayer was at 5 AM, the time between them will be 12 hours, which can be divided into three parts of four hours each. The first one-third is from 5 PM- 9 PM, the second one-third is from 9 PM-1 AM, and the last one-third is from 1 AM-5 AM.  

The best deeds in the last one-third of the night are prayer, supplication, seeking forgiveness, and reciting the Holy Quran, and Allah has commanded His Messenger Muhammad (PBUH) to pray additional prayer at night saying in Aya (79) of Surat Alisraa {And from the night pray Tahajjud with it, as additional for You, it is expected that Your Lord will raise You to a praiseworthy place}, and Aisha, May Allah be pleased with her, reported: "The Prophet (PBUH) used to offer thirteen Rak'ahs of the night prayer and that included the Witr and the two Rak'ahs (Sunnah) of the Fajr prayer" (Sahih Albukhari 1140), and as narrated by Abu Hurayrah: "The Messenger of Allah was asked as to which prayer was most excellent after the prescribed prayer, and which fast was most excellent after the month of Ramadan, He said the most excellent prayer after the obligatory prayer is prayer during the night, and the most excellent fast after Ramadan is Allah's month Almuharram" (Sahih Muslim 1163), and it is best to engage in seeking forgiveness and supplication, as Allah describes the righteous in Ayat (17,18) of Surat Aldhariyat {They used to sleep little in the night, and in the hours before dawn, they used to ask forgiveness}.

And Allah praises the believers in Aya (16) of Surat Alsajdah saying {Their sides remain apart from their beds, they call their Lord in fear and hope, and they spend from what We have provided them}, so their sides forsake their beds at night to remember Allah whether during the night prayer or without prayer and they call their Lord in fear of His punishment and hope of His mercy and reward.

 And among the best deeds in the last one-third of the night is reciting the Holy Quran, and the best recitation is that which is done during prayer, as the reward will be according the extent of recitation and humility, so the more one recites, the greater the reward, as Abdullah bin Amr bin Al-As narrated that the Prophet (PBUH) said: "If anyone prays at night reciting regularly ten verses, he will not be recorded among the negligent, if anyone prays at night and recites a hundred verses, he will be recorded among those who are obedient to Allah, and if anyone prays at night reciting one thousand verses, he will be recorded among those who receive huge reward" (Sunan Abi Dawood 1398). And Ibn Umar reported: "A man asked the Messenger of Allah (PBUH) about the prayer at night, the Messenger said prayer during the night should consist of pairs of Rakh'ahs, but if one of you fears morning is near (the Fajr prayer), he should pray one rakh'ah which will make his prayer an odd number for him" (Sahih Muslim 749).