Imām ar-Raghib said:
رمضان هو الرمض أي شدة وقع الشمس، والرمضاء شدة حر الشمس، و رمضت الغنم: رعت في الرمضاء فقرحت أكبادها. و سمي رمضان لأنه يرمض الذنوب أي يحرقها.
Ramaḍān is taken from the word ramad which means that which is intensely or vehemently heated by the sun. And the word ramdhaa means the intense heat of the sun. [The Arabs used to say about] the sheep that they were 'burned (ramidat) while they were grazing under the scorching heat of the sun to the extent that their livers became damaged (by the intense heat of the sun). Ramaḍān was named such because it burns the sins of the believers. 
Imām al-Zamarkhshari wrote:
لما نقلوا أسماء الشهور عن اللغة القديمة سموها بالأزمنة التي وقعت فيها فوافق هذا الشهر أيام رمض الحر فسمي رمضان
''When they changed the names of the months from the ancient language, they named them according to the seasons in which they fell, and this month fell in the days of intense heat and that is why it was named Ramaḍān''. 
Imām Qurtubi narrates:
إنما سمي رمضان لأنه يرمض الذنوب أي يحرقها با لأعمال الصالحة
''It (this month) was named Ramaḍān because it burns the sins of people with righteous deeds''. 
How does Allāh burn our sins?
The Prophet is reported to have said: “…Whoever draws nearer (to Allāh) by performing any of the (optional) good deeds in (this month) shall receive the same reward as performing an obligatory deed at any other time, and whoever discharges an obligatory deed in (this month) shall receive the reward of performing seventy obligations at any other time… ” [Narrated by Ibn Khuzaymah]
Therefore one of the main ways in which Allāh eradicates and deletes our sins and wrong doings is by multiplying our deeds in the month of Ramaḍān and erases our sins because the hasanat (good deeds) eliminates the sayyi'aat (bad deeds).
May Allāh destroy by the light of His raḥmah all our past sins, and may He make all of us among His servants who receive the glad tidings of forgiveness.
Please keep me in your sincere du'ā's and forgive any mistakes I may have committed.
 Mufradat al-Qur'an by Imām ar-Raghib p 203
 Al-Kashaf 1/171, Zad al Maseer 1/187, Majma' al-Bayan 1/275, Qurtubi 2/171
 Tafseer al-Qurtubi 2/271, Fatul Bayan 1/293