There is a Hadith in Sahih Bukhari:
Hadhrat Abdullah Bin ‘Abbas (May Allah be well pleased with them) narrates from the Holy Prophet (Sallallahu alaihi wa sallam) that He (Sallallahu alaihi wa sallam) said: There is no good deed which is superior to the deeds done in these days. The Companions asked: What about Jihad? The answer was: Not even Jihad except the person who strives in the path of Allah Most High endangering his life and property and does not return with anything.
(Sahih Bukhari, Hadith No. 926)
There is a Hadith in Shu‘abul Iman:
Hadhrat Harun Bin Moosa says: I heard Hadhrat Hasan (May Allah be well pleased with him) narrating on the authority of Hadhrat Anas Bin Malik (May Allah be well pleased with him): Every single day of the first 10 days of Dhul Hijjah is equal to 1000 days in reward and the day of ‘Arafah is equal to 10,000 days.
(Shu‘abul Iman, Hadith No. 3607)
Ghouse Azam Hadhrat Shaykh Abdul Qadir Jilani (May Allah be well pleased with him) has recorded a Hadith in “Al Ghunya Lit Talibi Tariqil Haqqi”:
Whoever spends in worship one night of the first 10 nights of Dhul Hijjah will get the reward of performing Hajj that year and the reward of performing ‘Umrah for the whole year and whoever fasts for one day in it will be considered to have performed worship of Allah Most High for the whole year.
(Al Ghunya Lit Talibi Tariqil Haqqi, Vol. 2, Pg No. 25)
Much stress has been laid on worship and obedience to Allah Most High in these 10 days.
The Holy Prophet (Sallallahu alaihi wa sallam) said:
When the first 10 days of Dhul Hijjah start, perform worship of Allah Most High, as these are the days, which Allah Most High has granted superiority and has made its nights sacred like its days.
(Al Ghunya Lit Talibi Tariqil Haqqi, Vol. 2, Pg No. 25)