Why is Laylatul Qadr an Important night for Muslims? Please quote from the Qur'an or Hadith.
Lailatul Qadr (Arabic: لیلة القدر) also known as Shab-e-Qadr,is the Night of Destiny, Night of Power, Night of Value, the Night of Decree or Night of Measures,
It is the anniversary of the night Muslims believe the first verses of the Quran were revealed to the Islamic prophet Muhammad.
Allah says in the Holy Quran:
We have indeed revealed this (Message) in the Night of Power:
And what will explain to thee what the night of power is?
The Night of Power is better than a thousand months.
Therein come down the angels and the Spirit by Allah's permission, on every errand:
Peace!...This until the rise of dawn!
—Sura 97 (Al-Qadr), āyāt 1-5
Therefore Allah himself puts this night better than a thousand months.
So worshipping on this night is better than if you worshipped for a thousand months (that’s about 83 yrs, and 4 months)! SubhanAllah!
Thus it would be foolish to miss this Night of Power.
Also the ayah 4 means that on this night, God’s decrees for the next year are brought down to the earthly plane. It is true that everything has been determined since the beginning of eternity and written down in the Preserved Tablet, but it is said that during this night, the Angels are informed of the destinies of the worshippers for the following year. It is a blessed Night. So, everything will be decreed on this Night. It is a night when fates are determined and it is a night of high standing.
Another important factor related to this night is that in it every decreed matter is conveyed as mentioned in the Holy Quran:
We sent it (Quran) down on a blessed Night. We were to warn [mankind]. Therein (in that Night) is decreed every matter of ordainment. Amran (i.e. a command or this Quran or His Decree of every matter) from Us. Verily, We are ever sending (the Messenger) (As) a Mercy from your Lord. He is the Hearing, the Knowing. Ad-Dukhaan 44: 3-6
Hope that answers your Questiion.
Laylatul Qadr is translated into the night of destiny, another translation is The Night of Power, there are many translations there is The Night of Decree, The Night of Value and so on. Laylatul Qadr is the night in which the Qur'an was revealed:
إِنَّآ أَنزَلۡنَـٰهُ فِى لَيۡلَةِ ٱلۡقَدۡرِ (١)
We have indeed revealed this (Message) in the night of Power: (1)
Surat Al Qadr Ayah 1
Laylatul Qadr is the night that is better than a thousand months:
لَيۡلَةُ ٱلۡقَدۡرِ خَيۡرٌ۬ مِّنۡ أَلۡفِ شَہۡرٍ۬ (٣)
The Night of Power is better than a thousand Months. (3)
Surat Al Qadr Ayah 3
The source of the above Ayahs are from Suratul Qadr/ 97
Laylatul Qadr In Quran
Verily! We have sent it (this Quran) down in the night of Al-Qadr , And what will make you know what the night of Al-Qadr (Decree) is? The night of Al-Qadr is better than a thousand months. Therein descend the angels and the Ruh by Allahs Permission with all Decrees, Peace! (All that night, there is Peace and Goodness from Allah to His believing slaves) until the appearance of dawn.
The night of Al-Qadr is better than a thousand months
When is Laylatul Qadr?
Narrated by Aishah (رضي الله عنها) Mohammed (صلى الله عليه و آله وسلم) says, Search for the Night of Qadr in the odd nights of the last ten days of Ramadaan.
Source: Small Khadem