what is atonement?

In Shrimad Bhagwatam’s 6th Canto, Shukdevji says to Maharaja Parikshit, “My dear King, if a person before His death, has not counteracted sins, committed in His lifespan, by way of atonement (prayashcita), as per the description of authorized Smritis, He will certainly enter the hellish planets after death and undergo terrible suffering under the hands of Yamadutas.”
Thus, one has to commit atonement as per the scriptures. Atonement counteracts the sins committed by a person. If a person does not perform atonements, He would have to undergo several ghastly punishments under the hands of Yamadutas.
If the person is impious and very sinful, the servants of Yamaraja, (called the Yamadutas), appear at the deathbed of the person in question and drag him forcibly from his body with ropes and chains. This scene so frightens the person that he literally dies of fright. They then pack up the subtle body of the person in a bag, where they take the soul, to the abode of Yamaraja for judgement. He is taken over long stretches of hot, dry sands, and along the way he is insulted in various ways by other horrible creatures and bitten by dogs. He suffers terribly on this journey.
Dharmashastras lay down various atonements for different kinds of sins. Atonements can be in the form of austerities, vows, visiting pilgrimages, performing nama japas etc. (You can refer Yagnavalkya Rishi’s Smriti with a Mitakshara tika to understand various types of atonements for various types of sins)
However, in the 6th Canto of Shrimad Bhagwatam, Shukdevji, says to Maharaj Parikshit that, atonements meant to neutralize impious actions are fruitive, hence, they will not release one from the tendency to act fruitively. Unless one, completely surrenders unto Shri Krishna (complete sharnagati), trying to counteract one’s sins is useless because this will not uproot one's desires. Thus even though one may superficially seem pious, he will undoubtedly be prone to act impiously. Therefore real atonement is enlightenment in perfect knowledge (Param Gnan, that He is a divine soul and not this body and perform Bhakti of Lord Krishna).
Those who have even once surrendered completely unto the lotus feets of Krishna, they do not see Yamaraja or his dutas even in their dreams. Thus, Sharnagati to the Adham-Udharan, Patita-Pavan, Daya-Sindhu (Lord Krishna) is the real atonement. I advise you to read the full Akhyan of Ajamila. After reading this Akhyan, you will understand the glory (Mahatmya) of Holy name of Krishna.
Lord Swaminarayan says that “If, a person with a corrupted mind believes, ‘Such a great Bhagvãn is patit-pãvan and adham-udhãran. So, why worry about slightly disobeying the niyam of dharma? After all, Bhagvãn is capable of granting kalyãn’. In this way, he does not hesitate in committing sins under the pretext of knowing God’s greatness. Such a person should be considered wicked and sinful. Also, even though he may superficially appear to be a Bhakta, he should not be considered a Bhakta, and a person should not remain in his company. Only a person who offers Bhakti to Krishna remaining in Dharma of His Varnashrama should be considered to be a Bhakta, and only his company should be kept.”