Ramadan kareem is of 30 days in total, divided into 3 Ashras (“Ashra’” is an arabic word for 10. So when we say an Ashra of Ramadan, we are pointing towards 10 days.). Each Ashra has it's own significance.
The first Ashra (first 10 days of Ramadan) is known as the period of Mercy. It is indeed the sign of ALLAH (SWT) Mercy upon us that we are blessed to observe Fast during Ramadan. it signifies the bestowments of ALLAH Almighty’s Mercy. There is a special Dua that our Prophet (S.A.W) has told us to recite in first ashra i.e:
1st-ashra-dua (Dua for 1st 10 Days)
يَا حَيُّ يَا قَيُّوْمُ بِرَحْمَتِكَ أَسْتَغِيْث
"Ya Hayyu Ya Qayyum bi rahmatika astaghees"
Translation: "O the Living, O the Eternal, I seek help in Your grace."
اے زندہ اور قائم رب! میں تیری رحمت کے حصول کی فریاد کرتا ہوں۔
Abu Huraira R.A related that the Prophet (P.B.U.H) said: Whoever fasts during Ramadan with faith and seeking his reward from Allah will have his past sins forgiven. Whoever prays during the nights in Ramadan with faith and seeking his reward from Allah will have his past sins forgiven. And he who passes Laylat al-Qadr in prayer with faith and seeking his reward from Allah will have his past sins forgiven (Bukhari, Muslim). Jazak Allah ul Khair ! Remember me and my family in your prayers.. :)