Catholic church believes that among other things, baptism is for remission of sins both original as well actual. Original in case of infants and original as well as actual in case of adults.
Baptism removes original sin:
Baptism is closely related to regeneration or ‘Born again” which is the transformation from death to life that occurs in our souls when we first come to God and are justified. He washes us clean of our sins (original as well as actual) as Psalm 51 points out:
Psalm 51:5 Look, I was guilty of sin from birth, a sinner the moment my mother conceived me.
Baptism gives us a new nature, breaking the power of sin over us, so that we will no longer be its salves but its enemies who must fight it as part of Christian life (Rom. 6:1-22; Eph. 6:11-17).
Jesus taught of this transformation through baptism of water and Spirit in John 3:5. In the water-and-Spirit rebirth that takes place at baptism, we are transformed from state of sin to the state of grace.
Peter mentioned this transformation from state of sin to grace when he exhorted people in Acts. 2:38-39.
Acts 2:38 Repent, and be baptised every one of you in the name of Jesus Christ for forgiveness of your sins; and you shall receieve the gift of the Holy Spirit'
Acts 2:39, For the promise is to you and to your children and to all that are far off, every one whom the Lord out God calls to him'
Peter explains the removal of original sin from our nature:
1 Pet. 3:20-21 ‘After they were disobedient long ago when God patiently waited in the days of Noah as an ark was being constructed. In the ark a few, that is eight souls, were delivered through water. 3:21 And this prefigured baptism, which now saves you – not the washing off of physical dirt but the pledge of a good conscience to God – through the resurrection of Jesus Christ,
Furthermore Paul notes that baptism has replaced circumcision.
In Col. 2:11 In him you also were circumcised – not, however, with a circumcision performed by human hands, but by the removal of the fleshly body, that is, through the circumcision done by Christ. 2:12 Having been buried with him in baptism, you also have been raised with him through your faith in the power of God who raised him from the dead.
If Paul meant to exclude infants, he would not have chosen circumcision as a parallel for baptism.
Augustine also taught that,
“ It is this one Spirit who makes it possible for an infant to be regenerated ... when that infant is brought to baptism; and it is through this one Spirit that the infant so presented is reborn. For it is not written, ‘Unless a man be born again by the will of his parents’ or “ by the faith of those born again of water and the Holy Spirit’[John3:5]. The water, therefore manifesting exteriorly the sacrament of grace, and the Spirit effecting interiorly the benefit of grace, both regenerate in one Christ that man who is generated in Adam”(Letters 98:2)
Origen also wrote in the third century that 'according to the usage of Church, baptism is given even to infants'(Homilies on Leviticus, 8:3:11,AD 244).
The council of Carthage, in 253, condemned the opinion that baptism should be witheld from infants until the eight day after birth.
Later Augustine taught,'The custom of Mother Church in baptising infants is certainly not to be scorned ....nor is to be believed that its tradition is anything except apostolic' (Literal Interpretation of Genesis 10:23:39, AD 408)